Argentina international Aguero had been stuck on 199 since he notched in the Carabao Cup final victory over Arsenal in February, but he finally added to his tally in the first half to put Chelsea on the path to defeat in its first competitive match under Maurizio Sarri.
The 30 year-old looked sharp and slotted home his second after the restart to ensure the Premier League champion started the new season with silverware.
Aguero's movement enabled him to find gaps in Chelsea's defence, which has switched to a back four after Antonio Conte's departure, and served to highlight the Blues' shortcomings in the final third.
Despite the absence of star players like Kevin De Bruyne, Raheem Sterling, Eden Hazard and Thibaut Courtois, the intensity was high in the opening stages.
City got on the front foot and took the lead inside 13 minutes when Phil Foden turned up the tempo by driving forward and feeding Aguero, who drifted into space 18 yards from goal and picked out the bottom-right corner.
Chelsea did not have its first touch in the opposition box until the 25th minute and the move ended with Alvaro Morata firing high and wide, the Blues struggling to break City down as the pace of the game subsided.
A delightful pass around the back of David Luiz from Foden gave Aguero the chance to get his second five minutes after the restart, but Willy Caballero did enough to force him wide and he could only find the side-netting.
Aguero was not to be denied eight minutes later, though, as he darted behind David Luiz and placed Bernardo Silva's neat pass beyond Caballero to put the result beyond doubt.
City could have added several more but a combination of poor finishing and some fine goalkeeping from former City man Caballero kept the scoreline respectable.
The protracted negotiations to bring Sarri in from Napoli severely restricted his time to start implementing his philosophy on the Blues - he was only appointed three weeks ago.
His high pressing and expansive style drew lofty praise from Guardiola after their two Champions League meetings last season, but Chelsea seemed a poor imitation of the Catalan's well-oiled City machine at Wembley.
Moving away from a three-man defence means players adapting to slightly different positions and a new shape, and some fine-tuning is required before they can really show what they could be capable of this season.
All five of Foden's Premier League outings last term came off the bench, but he produced a mature display that suggested he is ready to push for a starting berth. The 18-year-old showed an ability to change gears and lead City forward from midfield, as he did to set up Aguero for the opener. He was replaced by Brahim Diaz with 14 minutes remaining.
After struggling for consistency during his first season at Stamford Bridge, Antonio Rudiger failed to inspire confidence on Sunday. The centre-back's poor decision-making left Aguero in space to score the opener, while sitting too deep gave the Argentina international a chance to get a second shortly after the restart. Fortunately for the Germany international, he got away with his error the second time around.
City will be back in London to begin its Premier League title defence against another team entering a new era in Unai Emery's Arsenal, while Chelsea finishes its International Champions Cup campaign at home to Lyon before taking on Huddersfield Town on Sunday (AEST).