Second-half strikes from Yaya Toure and Aleksandar Kolarov after Swansea's Wilfried Bony had cancelled out Fernandinho's early opener helped City record their fifth consecutive Premier League win.
Bony grabbed a stoppage-time consolation and his second of the match with a skidding drive into the bottom corner, but there was to be no dramatic rescue for Swansea who are now without a win in six Premier League games.
City moved to the top of the table with 44 points from 20 games, two clear of Arsenal who can retake the lead with victory at home to Cardiff City later on Wednesday.
Manchester City, who have now recorded back-to-back away league wins for the first time this season, have taken 25 points from their last 27 and scored 57 goals in the opening 20 games to lay down a marker in the congested tussle at the top of the table.
"The character of the team in the second half to go and score another goal (after Swansea equalised) was very important," City manager Manuel Pellegrini told the BBC.
"You must not only play good football, you must have the character to try to recover when these things happen...
"It is satisfying because in the Premier League the last four games we play away, we have won three and drawn one, we must continue in the same way."
Swansea's home form has been their Achilles heel this season, having recorded only two wins at the Liberty Stadium, and coming into the game memories were still fresh of their 3-0 defeat in the reverse fixture last month.
Injuries to key players Michu, Michel Vorm and Nathan Dyer did not help their cause against the league's most impressive array of talent.
City started brightly and made their superiority tell in the 14th minute when Fernandinho, left unmarked on the edge of the area from a corner, drilled home with a raking low drive.
They took their foot off the gas, however, as the rain lashed down in south Wales, allowing Swansea to claw a foothold in the game and equalise in first-half stoppage time.
Bony, who looked to be in an offside position, got between Vincent Kompany and Pablo Zabaleta to head home an Angel Rangel cross.
At that point it looked as if City's suspect away form, having already lost four times on the road, may come back to haunt them, but nerves were steadied with a typically emphatic strike from midfield powerhouse Toure.
He picked up the ball on the edge of the box and spun away from two defenders before firing low into the bottom corner, a moment of quality that framed the difference between the two sides.
City's third had an element of good fortune about it as Kolarov's powerful strike from the edge of the area, after a lung-busting burst forward down the left flank, found the net due to poor keeping from Gerhard Tremmel.
Bony, by far Swansea's most threatening player on the day, smacked home a skidding drive that seemed to pick up pace of the slippery turf, but there was to be no dramatic finale.
"I think once again the performance was good, especially in the first half, but if you concede three goals to an opponent like Manchester City, it is very unlikely you will get anything from the match," Swansea City manager Michael Laudrup said.