City put their 3-1 loss at Ajax behind them with a 1-0 success at home to Swansea City in the Premier League's longest-ever game, while Arsenal celebrated Jack Wilshere's return from a 17-month lay-off by edging bottom club Queens Park Rangers by the same scoreline.
Defending champions City moved up to second place and closed to within a point of leaders Chelsea, who host third-place Manchester United on Sunday, while Arsenal climbed to fourth.
"It was important to get three points today after defeat in mid-week. We did not play well in the first half because we were so tired and we were better in the second half," said City coach Roberto Mancini.
"In the end, the only important thing is the result. If you win, you are the best manager; if you lose, you are the worst."
It took City 38 minutes to register a shot on target against Swansea in a lacklustre first half at Eastlands.
Swansea looked more likely to take the lead, but their clearest opportunity saw Joe Hart race from his line to save at the feet of the advancing Michu.
Spanish midfielder Michu drew Hart into action again with a downward header in the 59th minute but, two minutes later, Mancini's side struck.
Gael Clichy was allowed to carry the ball infield before finding Carlos Tevez, and the Argentine sent a shot dipping into the bottom-left corner to end a personal run of eight games without a goal.
Swansea goalkeeper Michel Vorm had to be stretchered off after appearing to hurt his groin as he tried to reach Tevez's shot, while City defender Micah Richards also had to leave the fray with a leg injury.
The stoppages meant that over 12 minutes of injury time were played – breaking the Premier League record – but City managed to keep their slender lead intact.
At the Emirates Stadium, Arsenal were made to wait until the 84th minute before Mikel Arteta's goal took them past QPR and enabled them to snap a two-game losing streak.
"We played quite well but lacked a little bit of the confidence you miss when you have lost two games," said Arsenal coach Arsene Wenger, whose side had lost to Norwich and Schalke in their previous two outings.
"A draw would have been a big disappointment, but if we had lost today it would have been a crisis."
Wilshere made his first appearance since missing the whole of last season through injury and Bacary Sagna also returned, but despite controlling the game, the hosts squandered opportunities throughout.
The momentum finally tilted in Arsenal's favour 10 minutes from time when QPR centre-back Stephane Mbia was sent off for petulantly kicking out at Thomas Vermaelen.
Arteta tucked home from close range four minutes later, amid suspicions of offside, and despite a flurry of late chances for the visitors – notably when Jamie Mackie shot straight at Vito Mannone after a mazy run – Arsenal survived.
"It was amazing to be back – words cannot describe it. I was just running around, smiling," said Wilshere, who played for 67 minutes.
"Last time I played it was with [Cesc] Fabregas and [Samir] Nasri – now it's with Arteta and Santi Cazorla, who are great players too. It's like a new team and I'm like a new player."
Fulham climbed to sixth after sharing six goals with Reading in an extraordinary 3-3 draw at the Madejski Stadium.
After falling behind to a stunning long-range strike by Mikele Leigertwood, Fulham hit back through substitute Bryan Ruiz and then pulled ahead in the 77th minute when Chris Baird glanced home a header from Ruiz's corner.
Gareth McCleary equalised for Reading in the 85th minute before Dimitar Berbatov restored Fulham's lead three minutes later, only for Hal Robson-Kanu to snatch a share of the spoils for the hosts by bundling home from close range in the last minute.
Elsewhere, a superb volley by Ivan Ramis set Wigan Athletic on their way to a 2-1 win at home to West Ham United that sent the Latics up to 15th, while Stoke City and Sunderland drew 0-0 at the Britannia Stadium.
Earlier, Norwich frustrated former coach Paul Lambert by holding Aston Villa to a 1-1 draw at Villa Park that left the Midlands club one place above the relegation zone. – AFP