Match ends, Manchester City 2, Swansea City 1.
Kelechi Iheanacho's injury-time deflection helped Manchester City return to the top of the Premier League as they beat managerless Swansea.
The hosts, who lost at Stoke a week ago, struggled against the Swans, who sacked ex-boss Garry Monk on Wednesday.
And after Wilfried Bony lost Ashley Williams to score against his former club, Bafetimbi Gomis' late equaliser looked like it would earn a point.
But there was still time for Yaya Toure to curl in off Iheanacho.
The hugely fortunate strike was a severe blow to a rejuvenated Swansea, who were led by caretaker boss Alan Curtis and created the better chances.
Yet after an almost perfect game plan, where Gomis came off the bench late on to end an 11-game goal drought in the league, Swansea slumped to a third consecutive defeat.
The result means the visitors have won one of their last 12 league games and after Bournemouth's win over Manchester United, slip to 16th in the table, a point above the relegation zone.
Swans players show they give a Monk-eys
Monk was sacked despite leading Swansea to their highest Premier League finish last season, and former Wales international Curtis said the team felt like they had let down their previous manager, intending to "go a small way to rectifying that" at Etihad Stadium.
After ensuring that Manchester City's Joe Hart was the busier goalkeeper, they succeeded.
With Gomis dropped to the bench and Gylfi Sigurdsson acting as an auxiliary centre-forward forward, this was a performance which combined defensive discipline and the heart that has perhaps been missing in Swansea's recent poor run.
It will certainly give hope to the incoming boss, with AEK Athens manager Gus Poyet among those linked with the job.
The only disappointing aspect from a Swansea point of view was City's first goal, as their normally reliable captain Ashley Williams failed to keep track of Bony's movement from a corner, allowing the Ivorian to score his seventh of the season with an easy header.
Other than that, Lukasz Fabianski was rarely troubled in the Swansea goal with Wayne Routledge and Sigurdsson drawing decent saves from Hart.
The stage was set for a late intervention as Gomis timed his run perfectly to beat Hart at the near post after coming on seven minutes earlier.
However, Swansea could do little to stop the winner as Toure cut in from the right and watched as his left-footed effort went in off Iheanacho's back.
Man City look laboured after Euro win
Manchester City will care little about Swansea's plight as they went above previous leaders Leicester, who face Chelsea on Monday, and Arsenal, who visit Aston Villa on Sunday.
Manuel Pellegrini's team now lead the Foxes on goal difference, with the Gunners two points behind.
But after topping their Champions League group with a 4-2 win over Borussia Monchengladbach on Tuesday, City's Chilean boss will be concerned by the lack of verve shown by his side, who did not have much intensity and purpose for long periods.
Kevin de Bruyne, who played in the victory over the Bundesliga side, was dropped to the bench despite some leading performances this season, and it appeared that the hosts missed the Belgian's guile.
David Silva looked like he is still working his way back to full sharpness after an injury lay-off while Raheem Sterling was well shackled by Swansea right-back Angel Rangel.
In the end, Pellegrini will be content to have earned three points, but Manchester City will need to improve for their crucial trip to Arsenal on 21 December.
Man of the match: Gylfi Sigurdsson
Manchester City boss Manuel Pellegrini: "I think the three points were very important, more than the way we played. I knew it would be difficult because we had three or four players who couldn't recover from the last game.
"Swansea played very well and it's not the way we want to win. Now we have a week to recover - we have played too many games with 13 or 14 players."
Caretaker boss Alan Curtis: "We certainly deserved to get something out of the game, and when we equalised I thought we were would hang in there. We probably did create more chances than City, that's the difference between the teams at the top of the league and at the bottom.
"We have been struggling with our form, but that's the standard we have to set between now and the end of the season."
Stats you need to know
- Manuel Pellegrini's side have won 14 and lost two of their last 16 Premier League home games.
- Swansea have won just one of their last nine Premier League away outings (W1 D2 L6).
- Wilfried Bony has scored five goals in the last four Premier League meetings between Manchester City and Swansea, (three for Swansea, two for Man City).
- Since his debut in August 2013, no Man City player has made more assists in all competitions than Jesus Navas (27 - level with David Silva).
- Bafetimbi Gomis ended a run of 836 minutes in all competitions without a goal for Swansea.
Manchester City travel to Arsenal a week on Monday, before hosting Sunderland on Boxing Day and have a trip to Leicester on 29 December. Swansea have two home games to come, against West Ham on 20 December and West Brom six days later.
- 3SagnaBooked at 60mins
- 20MangalaBooked at 77mins
- 42Y Touré
- 21SilvaSubstituted forDe Bruyneat 68'minutes
- 7SterlingSubstituted forDelphat 45'minutes
- 14BonyBooked at 58minsSubstituted forIheanachoat 84'minutes
- 17De Bruyne
- 3TaylorBooked at 43mins
- 7BrittonSubstituted forMonteroat 75'minutes
- 4Ki Sung-yueng
- 10A AyewSubstituted forGomisat 83'minutes
- 23G Sigurdsson
- 15RoutledgeSubstituted forBarrowat 76'minutes
- Robert Madley
- Shots on Target
Second Half ends, Manchester City 2, Swansea City 1.
Attempt saved. Gylfi Sigurdsson (Swansea City) right footed shot from outside the box is saved in the bottom right corner. Assisted by Ashley Williams with a headed pass.
Attempt blocked. Angel Rangel (Swansea City) right footed shot from the right side of the box is blocked. Assisted by Modou Barrow.
Goal! Manchester City 2, Swansea City 1. Yaya Touré (Manchester City) left footed shot from the right side of the box to the top left corner. Assisted by Jesús Navas.
Goal! Manchester City 1, Swansea City 1. Bafétimbi Gomis (Swansea City) right footed shot from the right side of the box to the top right corner. Assisted by Federico Fernández with a through ball.
Attempt missed. Bafétimbi Gomis (Swansea City) header from the centre of the box is just a bit too high. Assisted by Jack Cork.
Bacary Sagna (Manchester City) wins a free kick in the defensive half.
Foul by Neil Taylor (Swansea City).
Joe Hart (Manchester City) wins a free kick in the defensive half.
Foul by Bafétimbi Gomis (Swansea City).
Substitution, Manchester City. Kelechi Iheanacho replaces Wilfried Bony.
Substitution, Swansea City. Bafétimbi Gomis replaces André Ayew.
Attempt missed. Nicolás Otamendi (Manchester City) header from the centre of the box misses to the right. Assisted by Kevin De Bruyne with a cross following a corner.
Corner, Manchester City. Conceded by Ki Sung-yueng.
Attempt blocked. Wilfried Bony (Manchester City) right footed shot from outside the box is blocked. Assisted by Yaya Touré.
Foul by Fabian Delph (Manchester City).
Jack Cork (Swansea City) wins a free kick in the attacking half.
Attempt missed. Fabian Delph (Manchester City) right footed shot from outside the box misses to the right. Assisted by Jesús Navas.
Attempt saved. Ki Sung-yueng (Swansea City) header from the centre of the box is saved in the bottom left corner. Assisted by Gylfi Sigurdsson with a cross.