Saturday's contest at the Etihad Stadium burst into life when Aguero broke the deadlock to become the Premier League's all-time leading non-European goalscorer on 124.
Liverpool were left facing a huge uphill battle when Mane was dismissed for raising his boot in a challenge for a bouncing ball with goalkeeper Ederson, who was taken off on a stretcher after prolonged treatment, but later confirmed to have escaped serious injury.
Gabriel Jesus' header doubled City's lead in the stoppage time that resulted from that delay and he scored again early in the second half to end any hopes Jurgen Klopp's side had of mounting a comeback.
Substitute Leroy Sane capped a brilliant team move and superb display from the hosts by netting an excellent brace, bringing to an end Klopp's impressive record against City, having enjoyed a return of 10 points from his previous four matches with them. Klopp also endured the joint-heaviest defeat of his managerial career.
The victory takes Pep Guardiola's men to the summit for at least a few hours, with their opponents now three points back following a first loss of the campaign.
Without the injured Vincent Kompany or suspended Raheem Sterling, City were initially put on the back foot by a visiting line-up still devoid of wantaway forward Philippe Coutinho's services.
Nicolas Otamendi's clumsy challenge on Mohamed Salah gave the visitors an early sight of goal from a free-kick just to the right of the penalty area, but Alberto Moreno's shot struck the two-man wall.
City responded well and Kevin De Bruyne called compatriot Simon Mignolet into action at the other end, the Belgian goalkeeper making a solid save from the midfielder's powerful low shot.
Mignolet was also equal to Fernandinho's skidding effort in the 13th minute as City began to emerge as the greater attacking force.
And the breakthrough came when Liverpool's defence was cut open by Kevin De Bruyne's throughball and Aguero coolly rounded Mignolet before slotting home his sixth goal in as many home Premier League games against the Reds.
Mane threatened an instant riposte with a surging run, which Fernandinho brought to a halt by foul means just on the edge of the box, earning a booking for his troubles.
Emre Can was wasteful with the set-piece and City breathed another sigh of relief when Ederson saved smartly at Salah's feet soon after.
It was Liverpool's turn to fret next when Ragnar Klavan was caught in possession deep in his own half by Jesus, who forced a corner from which John Stones drew a reflex stop from Mignolet.
The visitors' task was made all the more difficult when Mane saw red following his challenge on Ederson, ending both players' outings, with Claudio Bravo introduced for City.
And Guardiola's side made their numerical advantage count when Jesus, who had already seen a goal ruled out for offside, headed in the second from the impressive De Bruyne's assist.
Liverpool were evidently deflated and the game was put beyond them when Aguero selflessly squared for Jesus, taking Mignolet out of the equation and leaving his team-mate with a simple finish.
The best was still to come from City's perspective, with Sane – on for Jesus, substituted with an eye on Wednesday's Champions League match at Feyenoord – putting the finishing touch on a flowing move before adding a fifth by arrowing a stunning left-footed strike into the top corner.
Liverpool, meanwhile, will host Sevilla in midweek nursing the heaviest loss of Klopp's tenure.
