The visiting Swans held their own during the opening 45 minutes and went into the break 0-0.
However, just before the hour mark Edin Dzeko opened the scoring from close range after Michel Vorm had parried a shot.
Aguero replaced Nigel De Jong shortly after and soon claimed his first City goal by turning in Micah Richard's drilled cross at the back post after 68 minutes.
The £35m signing then turned provider in the 71st minute, hooking back from the byline for midfielder David Silva to fire into the roof of the net.
As the final whistle approached, Aguero unleashed a right-footed effort from 25 yards which curled into the top left hand corner of the net.
Next up for City is a trip to Bolton Wanderers on Sunday while Swansea welcome Wigan Athletic to the Liberty Stadium a day earlier.