City took advantage of a rare missed penalty from Frank Lampard to claim victory at the Etihad Stadium and reduce Manchester United's lead at the top to 12 points.
Goals from Yaya Toure and substitute Carlos Tevez in the last half hour also strengthened City's grip on second place ahead of the third-placed Londoners.
With just 11 games left, it seems unlikely City will retain the title, although Mancini has vowed to fight on.
He said: "For us now it is not important to look at the table. Only to continue to work like we did here, to play well, to improve and to look at the table in one month.
"In football, it is finished when it is finished, the last minute of the last game. If we arrive at four games to go with United 12 points ahead, it is finished, but I think our job is to continue to work."
Mancini claimed Lampard's penalty was the game's pivotal point. Having been outplayed for the first half, Chelsea could have gone ahead in 51 minutes after Joe Hart brought down Demba Ba.
Lampard had scored his previous 10 spot-kicks, but Hart saved well to deny his England colleague his 200th Chelsea goal.
Mancini, who blasted Hart last week in light of recent mistakes, praised his keeper for recovering from his error.
The manager said: "I say to him everything when he did a fault. I think we can't concede a penalty like this with a kick (long ball) from 45 metres – he and Kolo (Toure) both made a mistake. But after, it was fantastic.
"I think it was important. Maybe the game could have changed, but also if they scored, we would have had another 40 minutes. We were playing well and we could have a chance to score other goals."
When asked if Hart could have been sent off, Mancini, perhaps referring to a red card for Vincent Kompany which was rescinded last month, said: "With our players it is possible. I joke – I don't think it was a red card. The ball went out."
The victory was City's first in the Premier League in over a month and restored confidence after the damaging loss at Southampton a fortnight ago, when Hart was at fault for one of the goals.
The keeper was pleased with his response after another potentially costly error.
He said: "Lamps is a big hero of mine and it was nice to save it, but I gave it away so I had to.
"Demba Ba was clever and left his knee in on me, so hopefully the save helped in the victory."
Chelsea's loss saw the pressure increase on interim manager Rafael Benitez, who was once again the target for abuse from fans.
They now trail City by seven points and Benitez accepted it was a damaging result.
He said: "Always when you lose, you are disappointed. This game was important for us, so I am more disappointed. We could have been closer [to City]. We have to carry on to try to win our games and fight for the top four."
Benitez, who is also challenging in the Europa League and FA Cup, made two big decisions by leaving heavyweights John Terry and Fernando Torres on the bench.
The Spaniard said: "We are playing too many games, games each three days. You have to manage your squad.
"Some players have fresh legs and you can play them."