By FOX Sports staff
Heading into the clash at Old Trafford with the scores 1-1 on aggregate, United took the lead three minutes after the break when Sergio Ramos inadvertently prodded a Nani cross past his own goalkeeper.
However, the Red Devils then found themselves down to ten men when Nani was issued a straight red for a high challenge on Alvaro Arbeloa, although replays suggested he had no intent to go catch his opponent with his studs and was merely going for the ball.
With the numerical advantage, Real duly equalised in the 66th minute when substitute Luka Modric netted with a cracking effort from the edge of the area, before Cristiano Ronaldo netted what proved to be the winner three minutes later when he slid in at the far post to convert a Gonzalo Higuain cross.
Here, FOX Sports breaks down where Tuesday's game was won and lost.
With Rio Ferdinand and Nemanja Vidic reunited in the heart of defence, United looked very steady at the back and the latter even posed a real threat at the other end of the ground, hitting the post with one header and testing Diego Lopez with another.
Although Rafael did expose his team at times as he regularly ran out of position, he provided the hosts with plenty of energy and drive down the right, and - at times - negated Real's numerical advantage it took two men to cope with his bursting runs.
It was Patrice Evra, however, who was most vulnerable for United, and it's no surprise the build-up to Ronaldo's winner came down his side.
De Gea - 7 | Rafael (off 87') - 8 | Ferdinand - 7 | Vidic - 7.5 | Evra - 6
In his 1000th appearance in a United shirt, Ryan Giggs rolled back the years with a sparking display, giving Fabio Coentrao a real headache, while Nani, up till the point where he was handed his marching orders, was equally effective down the other flank.
Michael Carrick too was steady in the engine room although he probably could have done better to prevent Modric from getting his shot away and equalising for Real.
Tom Cleverley, employed in a more-withdrawn role than he usually is, was also very impressive, especially in the first half when he got right into his opponents' faces and won possession in a number of crucial areas for the hosts.
Giggs - 8.5 | Carrick - 7 | Cleverley (off 73') - 8 | Nani - 7.5
Plenty of eyebrows were raised when Danny Welbeck was once again named in the starting XI to face the mighty Real, but he justified Sir Alex Ferguson's faith by putting in another impressive display.
The England international caused real problems for the Real defence with his pace and off-the-ball running, and he could really blossom into a world-class striker if he works on his finishing and movement inside the area.
Robin van Persie, however, failed to reach the lofty standards he has set for himself as he struggled to get into any real scoring positions, even though his link-up play was excellent.
Welbeck (off 81') - 8.5 | Van Persie - 7
One wonders what Wayne Rooney's long-term future is at Old Trafford after he was forced to settle for a place on the bench, and missed a gilt-edged chance to make it 2-2 shortly after coming on when he sent a half-volley from six yards out way over.
Ashley Young and Antonio Valencia were also brought on late in the game but had minimal time to make an impact.
Rooney (on 73') - 6.5 | Young (on 81') - N/A | Valencia (on 87') - N/A
Lopez got the game off to a shaky start as he twice failed to hold on to routine catches, although he made up for it by denying United on the rebound.
Nonetheless, he gradually gained confidence and preserved Real's lead towards the end of the game, making stunning saves to keep out close-range headers from Carrick and Vidic.
Although he scored an own-goal, Ramos' was immense at the back for Real but, like in recent weeks, his centre-back partner Raphael Varane stole the show with another display of his precocious talent, reading the game brilliantly and halting a couple of United attacks with perfectly-timed sliding challenges.
Down the left, Coentrao had a busy time keeping track of both Rafael and Giggs but coped admirably well, but Arbeloa was struggling to make an impact at right-back, until his determination to win the ball inadvertently saw him get Nani sent off.
Lopez - 8.5 | Arbeloa (off 59') - 6.5 | Varane - 8 | Ramos - 7.5 | Coentrao - 7
While he wasn't really noticeable, Sami Khedira did a decent enough job trying to win possession for his team and pass it on to Xabi Alonso, who hardly misplaced a pass all evening long although his delivery was not as incisive as it usually is.
Further up the field, Mesut Ozil showed plenty of energy but ultimately struggled to get the better of his direct opponent, and was unsurprisingly replaced in the 71st minute.
Khedira - 6.5 | Xabi Alonso - 7 | Ozil (on 71') - 7
Ronaldo may have received his fair share of criticism throughout his career, but he deserves applause for his display on Tuesday. Even though he was tightly marked throughout the 90 minutes, he never stopped trying to break free and was always ready to test De Gea from distance.
Likewise, Higuain also worked hard despite coming up against a stern United defence and it was fitting that both of them linked up for what proved to be their side's winning goal.
Angel Di Maria, however, had a disappointing outing which was ended prematurely when he picked up an injury and had to be replaced before the break.
Di Maria (off 45') - 6.5 | Ronaldo - 8 | Higuain - 7.5
Ferguson may be fuming at the referee following Tuesday's game, but he will probably be slightly upset at himself for not pursuing Modric and letting him join Los Blancos in the end.
Although the Croatia international is yet to force his way into coach Jose Mourinho's starting XI, he showed his class when he came off the bench and immediately dictated proceedings, before popping up seven minutes after entering the field to equalise with a fantastic strike.
Kaka, coming on for the injured Di Maria, was also serviceable in the attacking third, while Pepe, although on for just over 20 minutes, provided excellent cover at the back and made a number of good blocks to prevent crosses from entering his area.
Kaka (on 45') - 7 | Modric (on 59') - 7.5 | Pepe (on 71') - 7