It was the penultimate game of the 2014/15 campaign and Manuel Pellegrini's side knew there was no chance of retaining the title.
Chelsea had already been confirmed champions by the time the Blues travelled to South Wales, but finishing runners-up was still on the cards.
It turned out to be an entertaining afternoon at the Liberty Stadium, and City took command in the first-half with goals from Yaya Toure and James Milner.
However, the Swans halved the deficit on half-time and levelled just past the hour as Garry Monk's side chased a Europa League spot.
But City finished strongly with a second for Yaya Toure and an added time strike from Wilfried Bony in added time.
Relive the game courtesy of the classic highlights above!