Only four points separate third-place City and leader Chelsea, but only due to the team scraping by.
The Champions League has been less forgiving, with City's prospects looking bleak after two losses and a draw — draining the team of confidence and creating the impression of instability.
Disquiet in the dressing room is emerging, with frustrations over changing formations voiced by Micah Richards. The City defender had claimed the defence struggled due to Mancini's shifting the formation in the 3-1 loss at Ajax on Wednesday — from four to three at the back.
"If you are a top player it is not important what system you use," City manager Roberto Mancini said Friday, a day before the home match against Swansea. "If you don't understand a system like that, you cannot play for a top team."
Such a putdown could be Mancini reasserting his authority on the team in a bid to prevent City from completely imploding.
"If we allow one defeat to alter that, we would be really weak," Mancini said. "Strong teams can lose a game but it is important you understand the reasons, and what mistakes were made. You can learn from this and improve for the next game."
Swansea winger Wayne Routledge hopes they don't on Saturday.
"As footballers, they're in the higher echelons but sometimes you have games when it doesn't click," Routledge said. "That seems to be what happened the other night. It wasn't the usual Manchester City."
But the Premier League standings could look a lot more encouraging by the end of the weekend for City.
If City beats Swansea on Saturday and Manchester United inflicts leader Chelsea's first league loss the following day, the Manchester rivals will both only be a point behind the west London club.
The season was progressing serenely for Chelsea this season — on the field at least — until a first loss of the season against Shakhtar Donetsk.
"We have to make sure we correct it very quickly and that starts with the next game against United," Chelsea midfielder John Obi Mikel said. "They will be very dangerous as usual and, if we defend the way we did (against Shakhtar), it's going to be difficult for us.
"We have to defend as a unit, play together as a unit. As long as we do that on Sunday, we'll have a very good chance."
With John Terry serving his suspension for racial abuse, Chelsea will be without another veteran of United encounters. Frank Lampard is out for two weeks with a right calf injury.
But United hasn't won a Premier League match at Stamford Bridge in a decade.
"I don't think we've played badly," United manager Alex Ferguson said. "We have actually played well in the games we have lost only to get bad decisions against us."
Further down the standings in ninth, Arsenal needs to rebound quickly against last-place Queens Park Rangers on Saturday after successive losses in the Premier League and Champions League.
Arsenal manager Arsene Wenger is wondering where the team's dynamism has gone.
"Suddenly had two flat performances. It is difficult to explain," Wenger said. "We have hit the wall a little bit in the last two games, and just did not find our rhythm.
"But we have to just focus again on the quality of our game, the way we want to play, and not concede too much against who we play. With the quality (we have), the results will come back."
Also Saturday, Aston Villa hosts Norwich, winless Reading takes on Fulham, Sunderland is at Stoke and Wigan faces West Ham.
On Sunday, Brendan Rodgers will take charge of Liverpool for the first time in a derby against Everton, while fifth-place Tottenham is at Southampton and Newcastle hosts West Bromwich Albion.