United took an early lead in the 10th minute after Wayne Rooney rose highest in the City box to nod home Antonio Valencia's perfectly-weighted cross, before Vincent Kompany received his marching orders for a fairly innocuous two-footed challenge on Nani.
Buoyed by their numerical advantage, United piled forward and doubled their lead through a stunning volley from Danny Welbeck, before the young England international earned the Red Devils a penalty in the 39th minute after he was brought down by Aleksandar Kolarov.
Rooney's initial effort was saved, but he reacted quickest to nod home the rebound, giving United a 3-0 halftime lead.
However, City came out firing on all cylinders in the second half, and pulled one back just three minutes after the restart when Kolarov fired in a freekick from the edge of the area.
Sergio Aguero then gave City a glimmer of hope when he netted another, but United held on despite a nervous closing period to seal their progress into the fourth round of the FA Cup.
Here, ESPNSTAR.com takes a look at the players who took to the field on Sunday, including the return of a certain 37-year-old.
Costel Pantilimon - 6.5
City's Romanian reserve goalkeeper has been impressive in his brief outings for the Citizens, and even though he conceded three against United, he was left helpless by his defence on each occasion.
Even pulled off a good save to deny Rooney from the spot, although unfortunately for Pantilimon, the United striker managed to nod home the rebound.
Micah Richards - 8.5
Sterling performance from the robust defender, who held the City backline together after Kompany received his marching orders. Showed his versatility by starting off at right-back, before looking like a natural in the heart of defence, where he could eventually play permanently in the future.
Ended the game as a makeshift centre-forward, and gave Rio Ferdinand a couple of problems with his pace and strength.
Vincent Kompany - 6.5
The Belgian's outing was brought to an early and unfortunate end as he was sent off rather harshly for a two-footed challenge on Nani in the 12th minute. He did leap in with both feet, but he got plenty of the ball, and hardly any of the player.
Joleon Lescott - 6
Was culpable for United's opener when he failed to pick up Rooney's late run into the box, allowing the England international to leap above him, Kompany and Welbeck to nod the Red Devils into the lead.
Aleksandar Kolarov - 6.5
Kolarov endured a horrible start to the game, where he was constantly caught out by Antonio Valencia's pace and directness. The Serbian international also cost City a goal when he rashly challenged Welbeck in the box, handing United a penalty.
However, Kolarov recovered and had an excellent second half, putting City back in the game three minutes after the restart when he curled in a trademark freekick beyond the reach of Anders Lindegaard.
Nigel De Jong - 7
Like most of the City players, De Jong had an awful first half, leaving his back four exposed on several occasions.
However, he came back strongly after the restart and started to impose himself, putting in several strong-but-fair challenges in the middle of the park.
James Milner - 7.5
Another solid performer for City, Milner never stopped trying to push City forward, even when he was deployed at right-back after Kompany's red.
David Silva (off 46') - 7.5
City's brightest spark in the first half, it was somewhat surprising to see the dimuntive Spaniard withdrawn during the break. Perhaps the clearest sign from Roberto Mancini that the FA Cup just isn't high on his priorities this season.
Adam Johnson (off 46') - 7
Like Silva, Johnson's removal at halftime came as a real shock, especially considering he was one of City's main attacking threats during the opening period.
Gave Patrice Evra plenty of problems down the right, cutting in on his left foot and whipping in a number of dangerous deliveries.
Samir Nasri (off 82') - 3
The Frenchman touched the ball on a couple of occasions in the first half, and was virtually unsighted in the entire second half, right until he was replaced eight minutes from time.
Currently looking like a shadow of the player he was at Arsenal last season, and for now, he is struggling to justify his £25million transfer fee.
Sergio Aguero - 9
Aguero was an absolute handful for the United defence on Sunday, despite playing much of the game by himself up front.
Dropped deep to pick up the ball, before heading straight towards the United goal, at times forcing defenders to double-team him in a desperate bid to dispossess the Argentinean. Got on the scoresheet in the 64th minute when his firmly-struck shot was fumbled by Lindegaard back into his path, leaving him with an empty net to tap into.
Stefan Savic (on 46') - 8
The Montenegrin hasn't had many chances to prove himself this season, but he certainly showed what he's capable of in his 45 minutes on the Etihad pitch on Sunday.
Regularly booted away United crosses at the earliest opportunity, displaying an old-fashioned, no-nonsense approach to defending.
Pablo Zabaleta (on 46') - 7
It must be nice for City to have someone like Zabaleta to call on in reserve. Rock-solid in defence, yet capable of bombing forward and threatening in attack, the Argentinean's introduction was one of the main reasons for the Citizens' excellent second-half performance.
Owen Hargreaves (on 82') - N/A
Brought on eight minutes for time for a rare taste of action against the club he left in the summer. Minimal time to make an impact.
Anders Lindegaard - 6
After an impressive start to his United career, Lindegaard looked slightly shaky against Newcastle in midweek, and failed to fare any better against the Citizens on Sunday.
Nearly gave City an early opening when he allowed Aguero to chase down an attempted clearance, and flapped at a number of crosses. Probably could have done better for Kolarov's freekick, although it was a well-struck effort, but will have take the blame for City's second, when his weak parry fell straight at the feet of Aguero.
Chris Smalling - 7
A fairly decent return to action from Smalling after weeks out. Looked slightly off the pace at the start of the game, but recovered well, and showed poise and stability at the back.
Phil Jones - 7.5
Does Jones ever play two successive games in the same position? After a terrible display in the heart of defence against Newcastle, Sir Alex Ferguson shifted his young protégé out to the right, and he bounced back well with a good showing.
Bombed forward with regularity, showing good pace and strength, but was perhaps slightly untidy with his distribution.
Rio Ferdinand - 5
The veteran defender is starting to be more of a liability than a steadying influence at the back. Tried to be too clever on a number of occasions by playing long, diagonal balls out of defence, and ended up giving the ball straight to City.
Looked more interested in blasting his team-mates to cover up his own mistakes, and is currently a weak stand-in for the injured Nemanja Vidic.
Patrice Evra - 6.5
The Frenchman had a good opening period, constantly putting City on the back foot with his forays forward, and it was the cross he drilled in which led to Welbeck's excellent strike.
However, his suspect defending reared its ugly head once again in the second half, and he spent most of his time tugging back and hacking down opponents after they had gotten the better of him.
Antonio Valencia - 8.5
One of United's best on the afternoon, and looking truly comfortable playing in midfield, Valencia carved open the City defence with regularity in the first half, heading straight for the touchline before whipping in excellent deliveries.
It was his pinpoint cross in the 10th minute that led to Rooney nodding United into the lead.
Michael Carrick - 7.5
A tidy-if-unimpressive performance from the holding midfielder, who retained possession well and put in a number of excellent interceptions just as City were looking to come forward.
Still, Carrick will never truly establish himself as a United great, largely due to his inability to take a game by the scruff of its neck. Seems more content to play the obvious pass in hope a more creative team-mate will step up and create opportunities for their forwards.
Ryan Giggs - 8
It's a rare occasion to see Giggs start back-to-back games, especially considering Ferguson only saves him for the crunch games. However, with United struggling with injuries, the Welshman was fielded against City, just four days after playing in the game against Newcastle. And he justified his manager's decision to name him in the starting XI as he dictated proceedings for United in the first half as they dominated City.
Played a huge part in United's third as it was his killer pass through to Welbeck that resulted in his young team-mate being brought down in the box by Kolarov.
Nani (off 59') - 7
The Portuguese was fairly dangerous in the 60 minutes he was on the field, regularly looking to run at the City defence, although his touch was sloppy on several oocasions.
Was involved in the game's major talking point when a challenge on him by Kompany saw City's Belgian skipper get sent off, even though - for once - even Nani didn't seem to think it had been a foul, let alone a red card.
Wayne Rooney - 9
Rivaled Aguero for man-of-the-match honours, although Rooney probably just edges it as his contributions helped his team to the victory.
Scored the opening goal after the played a quick ball out wide to Valencia, before racing into the box, showing an excellent leap to out-jump Kompany, Lescott and Welbeck and heading home a perfect header into the top corner.
Added his second six minutes before the break when he tapped home into an empty net after his initial spot-kick had been saved by Pantilimon. Faded away in the second half, but was a main creative outlet for United for much of the game.
Danny Welbeck (off 75') - 8
Welbeck looks like he's slowly regaining the early-season form that saw him feature in Fabio Capello's England plans.
Was lively all afternoon, and scored the goal of the game when he pounced on Lescott's loose header, before swiveling and hitting a full-volley over his shoulder into the far corner. Possesses bundles of energy and is rightfully keeping Javier Hernandez and Dimitar Berbatov out of the starting XI at the moment.
Paul Scholes (on 59') - 7
In case you are still not aware of the news - nope, this is not an error. The little maestro is back for United until the end of the season, and he got straight into the thick of things immediately, linking up a number of intricate passing moves from United.
However, his half-season spent on the sidelines showed as his misplaced pass on the left wing led to City's second, but overall, it was a fairly neat performance from United's new No. 22.
Anderson (on 75') - 5
On the other end of the spectrum, one of the early-season pretenders to Scholes' crown had a terrible cameo appearance after being brought with 15 minutes remaining.
The Brazilian offered United nothing going forward, spending most of his time standing still and yelling for the ball. It'll be interesting to see how much he features for United over the next six months, especially with Scholes back and Tom Cleverley returning from injury.