Aguero fired Manchester City to the top of the table for couple of hours as they beat Wigan 3-0 in a 3pm kick-off at the Etihad Stadium.
But Manchester United responded in typically belligerent fashion in the teatime game, outscoring their city rivals with a Rooney-inspired 5-0 thumping of Bolton at the Reebok.
Having scored three in the 8-2 hammering of Arsenal in his last club game, the England striker made it back-to-back hat-tricks in another comfortable victory.
Rooney follows Les Ferdinand, Ian Wright and Didier Drogba in becoming only the fourth player in Premier League history to achieve the feat, part of an overall 18-goal tally for the Red Devils so far this season.
Indeed, Rooney has now scored eight goals this term, more than any top-flight side, with the exception of City, have managed between them, with Javier Hernandez adding two more at the Reebok on his first start of the campaign.
Aguero, meanwhile, has had no trouble adapting to life in England and his latest three goals mean he has scored six times in four games since his move from Atletico Madrid.
His effort contrasted with Carlos Tevez, who missed a penalty to add to being stripped of the captaincy this week.
Aguero scored his first to give City the lead in the 13th minute. David Silva was instrumental, selling his marker a dummy and passing to Aguero who shot low across the keeper and into the net for his fourth goal in three games.
City missed a chance to double their lead six minutes later when Tevez missed a penalty given for an Adrian Lopez foul on Silva. Ali Al Habsi dived to his right to save.
Aguero, though, got his second in the second half when he finished a slick passing move, slotting home first-time from Samir Nasri's inch-perfect low ball and he took little time to complete his hat-trick, converting Silva's pass.
Daniel Sturridge was a key figure as Chelsea won 2-1 at Sunderland to keep up the pressure on the leading two.
John Terry put the Blues ahead in the 18th minute when he gathered a cross on the left of the area from Sturridge and sent in a ball across the six-yard box.
The Black Cats failed to clear and when the ball came back to the England captain, he fired into the back of the net.
The Blues doubled their lead five minutes after the break, this time Sturridge turning scorer as he ran on to a long ball and back-heeled into the net despite the best efforts of Wes Brown to stop the ball crossing the line.
Sunderland pulled one back through Ji Dong-won in the final minute after he was left unmarked in the area but it was too little, too late.
Liverpool went 1-0 down through a penalty at Stoke when Jamie Carragher was adjudged to have fouled Jon Walters.
The Stoke forward appeared to go down a little easily after the former England defender put his arm around his waist. However, Walters got up to fire down the middle .
Liverpool responded, Jordan Henderson and Charlie Adam peppering the goal with Luiz Suarez then missing a great chance in stoppage time as the Potters held on.
Arsenal lifted the gloom with a 1-0 win against Swansea, who have still yet to score this season.
The Gunners, who fielded all five of their deadline-day signings, won thanks to an awful error five minutes before half-time by Michel Vorm.
The Dutchman gathered the ball and rolled it out but it hit the heel of team-mate Angel Rangel and Andrey Arshavin slid the ball home from a tight angle.
The Swans came within inches of equalising when Scott Sinclair's 25-yard free-kick hit the bar and went out.
Tottenham won 2-0 at Wolves, going ahead halfway through the second half when two recent arrivals combined.
Scott Parker, who joined last week from West Ham, poked the ball through for Emmanuel Adebayor who ran on to the ball and slotted home.
Harry Redknapp's side doubled their lead 10 minutes from time, Jermain Defoe firing home from close range.
Everton and Aston Villa drew 2-2 at Goodison Park.
Leon Osman put the Toffees ahead after being played in by Tim Cahill, only for Villa to equalise in the 63rd minute through Stiliyan Petrov's long-range shot.
The hosts regained the lead when Fabian Delph was penalised for a foul on Phil Jagielka and Leighton Baines fired home the spot-kick, but the visitors levelled when Gabriel Agbonlahor headed home Marc Albrighton's cross seven minutes from time.
On Sunday, West Brom earned their first win of the season after Peter Odemwingie capitalised on a defensive mistake to score the only goal in the match against Norwich at Carrow Road.
Fulham and Blackburn remain winless and rooted to the bottom of the table after they played out a 1-1 draw at Craven Cottage. Ruben Rochina and Bobby Zamora both scored brilliant individual efforts in the first half.
Arsenal 1-0 Swansea
Bolton 0-5 Man Utd
Man City 3-0 Wigan
Stoke 1-0 Liverpool
Sunderland 1-2 Chelsea
Wolves 0-2 Tottenham
Everton 2-2 Aston Villa
Norwich 0-1 West Brom