Goals from Kyle Walker, Raheem Sterling and Gabriel Jesus helped Pep Guardiola’s side to a 3-1 win, with Morgan Whittaker grabbing a late consolation at the Liberty Stadium.
The win was Manchester City’s 15th in a row in all competitions and took them past the previous record of 14 wins by English top-flight clubs in all competitions, jointly held by the Preston side of 1891-92 and Arsenal in 1987.
Guardiola made seven changes to the side that had beaten Liverpool on Sunday, as American goalkeeper Zack Steffen started behind an entire new back-four unit, with Rodri, Bernardo Silva, Ilkay Gundogan and skipper Sterling the only survivors of the Anfield victory.
Swansea, riding high in the Championship and eyeing a return to the Premier League, gave a first start to United States striker Jordan Morris following his January loan arrival from MLS side Seattle Sounders.
Morris had few chances to show his impressive pace in a first half which the visitors dominated and had chances to take the lead before it arrived from an unlikely source in the shape of Walker.
Swansea goalkeeper Freddie Woodman saved early efforts from Jesus and Gundogan as the pressure was cranked up.
Jesus and Aymeric Laporte then failed to find the target from gilt-edged openings and Ferran Torres brought two more stops from Woodman.
But the charmed life that Swansea’s goal had been leading was finally over after 30 minutes.
Walker’s cross was aimed towards forwards in the middle, but neither Torres nor Jesus could apply a touch and the ball evaded everyone to nestle in the far corner of Woodman’s net for only the fifth goal of the England defender’s City career.
Swansea responded well to falling behind and Connor Roberts sent over a cross which Jay Fulton headed narrowly wide.
Yan Dhanda’s chip also set up Jamal Lowe for a near-post effort which was blocked by Eric Garcia.
But Swansea hope was extinguished in brutal fashion immediately after the break.
Rodri split the Swansea defence within two minutes of the restart and Sterling swept home his 12th goal of the season.
Three minutes later Jesus rifled home to make it four goals in as many starts, his best run since scoring in seven straight starts between April and October 2019.
City had further chances to extend their lead, but the flow of the contest was interrupted by a raft of substitutions with Guardiola and Swansea’s Steve Cooper turning their thoughts to weekend league action.
There was a scare for Guardiola as Rodri limped off and a Swansea consolation when Whittaker claimed his first goal following his deadline day arrival from Derby.
Whittaker controlled Ryan Manning’s cross and fired past Steffen as the visitors conceded for only the fifth time in their 15-game winning streak.