In a game that was fantastic entertainment from start to finish, both sides swapped blows as the axis seesawed one way then another.
The Blues had to come from behind to lead, before being pegged back again by the Serie A leaders - until Aguero settled the tie with the sort of goal that has become his trademark over the years.
Raheem Sterling sealed a 4-2 win with a late strike to add to goals either side of the break from defenders Nicolas Otamendi and John Stones.
What a night and what a performance as City became the first English side to beat Napoli on their own soil.
Ilkay Gundogan, Danilo, Sterling and Aguero were all recalled at the expense of Kyle Walker, Bernardo Silva, David Silva and Gabriel Jesus.
City’s high press quickly put Napoli under pressure and forced one or two errors from the Italian side.
Leroy Sane’s burst into the box in the first few minutes caused a few nerves to jangle for the home support and Raheem Sterling was unlucky not to wriggle his way through the hosts’ defence moments later as the Blues took the game to their Group F opponents.
But Napoli were soon creating problems at the other end with their own brand of stylish passing and intelligent movement and a clever exchange between Dries Mertens and Lorenzo Insigne broke the deadlock on 21 minutes with the latter slotting past Ederson of the six-yard box.
It was a blow, but City know how effective Napoli can be with their tails up after the first meeting between the teams at the Etihad.
The Blues responded well and came agonisingly close to levelling when Sterling’s clever pass found Aguero who had peeled off his marker, but his shot was deflected inches past the post as it seemed he was finally going to set a new Club record.
No matter – City levelled minutes later as Gundogan’s sweet cross was headed home by Otamendi at the far post.
The Blues had taken the game by the scruff of the neck and were a coat of paint from taking the lead five minutes later as Otamendi first connected horribly with another Gundogan cross before John Stones thumped a header against Pepe Reina’s crossbar.
The next time Stones struck the bar – just three minutes after the break – he was celebrating his fourth Champions League goal of the season.
Leroy Sane’s corner was headed firmly towards goal by Stones who watched the ball hit the underside of the bar but bounce over the line to give City the lead and silence a partisan home support.
It was no more than the Blues deserved, either – but the hosts were far from finished as Insigne’s long-range shot struck the bar with Ederson beaten on 56 minutes.
It was the sort of breathless entertainment many had predicted and the game took another twist just past the hour-mark as Sane’s clumsy tackle on Raul Albiol was deemed a penalty that Jorginho calmly converted with 62 minutes played.
But the moment City fans had been waiting for finally came on 70 minutes with a goal that will be remembered for a long time.
A Napoli attack was cleared and Fernandinho played a peach of a pass to Sane who put on the afterburners and headed towards goal – as he was tackled, Aguero picked up the loose ball, continued towards goal before hitting a low shot past Reina to put the Blues ahead and set a new Club record of 178 goals.
It was a wonderful moment and a goal fitting of breaking a record – how relieved the Argentine must be to have finally achieved this momentous feat.
There were several chances for the Blues to increase the winning margin before Gabriel Jesus won possession and fed Kevin De Bruyne and the Belgian waited before playing in Sterling who buried a low shot in added time to put the icing on a wonderful performance by City.
Star man: Sergio Aguero
Who else but Kun would win the City Match Day App vote on a night to remember from the Argentine striker.
What it means…
City qualify for the Round of 16 with maximum points from four games and two games to spare. Shakhtar lead the race to finish in second spot.
The Blues also chalked up a 14th successive win and are now 21 games unbeaten in all competitions.
City host Arsenal on Sunday looking to consolidate top spot in the Premier League with a win over Arsenal. Nearest rivals Manchester United travel to reigning champions Chelsea.