Wilfried Bony scored near the end of each half but goals from Fernandinho, Yaya Toure and the left back were enough to secure a New Year's Day win for City.
Goals from Fernandinho, Yaya Toure and Aleksandar Kolarov secured three points for Manuel Pellegrini's side to give the club its first win at the Liberty Stadium.
Wilfried Bony grabbed two for the home side but it was in vain as City recorded another impressive victory.
The win took Manchester City back to the top of the table ahead of Arsenal's clash with Cardiff City later on Wednesday, while the Swans remain in mid-table but will be nervously looking over their shoulder at the bottom three.
Swansea boss Michael Laudrup was able to recall Angel Rangel and Wayne Routledge to his starting lineup, while the visiting team made five changes to the side that beat Crystal Palace.
Swansea created the first chance as Bony collected a pass from Jonathan De Guzman on the edge of the penalty area but his low shot clipped the post on its way to going wide.
City made the Ivorian pay for that miss almost immediately, as the club opened the scoring in the 14th minute through Fernandinho. Swansea failed to clear a right-wing corner and the loose ball dropped to the Brazil international, who fired through a crowd and into the back of the net.
Laudrup's side went close to an equalizer in the 25th minute when a flowing move involving Bony and substitute Roland Lamah - on for the injured Pablo Hernandez - released De Guzman in behind the Manchester City defense but the Dutch midfielder could not get the ball out of his feet and his scuffed shot was easily held by Joe Hart.
Both sides had chances to get the game's second goal before the break and it was Bony who produced a leveler for the home side. The forward got ahead of Pablo Zabaleta in the 44th minute to meet De Guzman's cross and head past Hart – although the 25-year-old appeared to be in an offside position when the ball was delivered.
Pellegrini's side restored the lead in the 58th minute, however, thanks to Toure's 10th league goal of the season. The midfielder created room for himself room inside the penalty area before his shot wrong-footed Gerhard Tremmel thanks to a deflection off Ashley Williams.
Kolarov then added the third goal eight minutes later with a great solo effort. The Serbian won the ball from Routledge inside his own half and ran unopposed to the Swansea penalty area, where he cut onto his right foot and fired past Tremmel – although the goalkeeper should have done better.
As Swansea continued to show endeavor, Bony missed a chance to reduce the deficit in the 72nd minute but he did net his second with a long-range strike in the second minute of injury time as the home side gained some reward.