French midfielder Nasri shone as City came from behind to edge out Swansea 2-1 in the Barclays Premier League with goals from Stevan Jovetic and Yaya Toure at the Etihad Stadium on Saturday.
It was only the champions' second win in seven games in all competitions and provided a timely lift, even though in title terms it merely prevented Chelsea extending an eight-point advantage over them.
Manuel Pellegrini's men now face a crucial home clash with German giants Bayern Munich on Tuesday knowing they have little room for error.
City's much-hoped for Champions League push is in a precarious state after a failure to win any of their first four Group E games.
City will exit the competition at the group stage for a third time in four attempts if they fail to beat Bayern and there is a winner in the game between CSKA Moscow and Roma.
Nasri said: "It was important to keep in touch with Chelsea, who look unbeatable at the moment
It was really important to win the game.
"It was a tough start, they scored an early goal, but we had a good reaction
We started to press high and play our game
It was good for the confidence as well because on Tuesday we have a tough game.
"We are really lucky to still be in with a chance of qualifying because, with two points and two games left, normally you are out.
"Now is our chance
We have to take it and play with nothing to lose.
"We can take a lot (from this win) but a game against Bayern Munich will not be the same as a game against Swansea
No disrespect to Swansea, who are a great team, but Bayern Munich have world-class players in every position."
City's recent problems, particularly in defence, looked to be continuing as Wilfried Bony celebrated signing a new contract by firing Swansea into a ninth minute lead.
The hosts' marking was poor as Bony found space in the area but the goal still owed much to skill as the striker deftly controlled Nathan Dyer's brilliant flick on his chest and then fired past Joe Hart.
City were sluggish early on but Jovetic levelled 10 minutes later when he got on the end of a wicked low cross from Jesus Navas.
The hosts then stepped up the pressure and hit the post - after a fingertip save from Lukasz Fabianski - through Gael Clichy.
The pressure paid off just after the hour as Toure, hinting at a possible return to form, powered forward in typical fashion to drive home the winner.
City's overall superiority arguably merited victory but Swansea had two late chances as Bafetimbi Gomis missed the target and a Jonjo Shelvey free-kick was deflected narrowly wide.
Despite the result, Swansea, who beat Arsenal in their previous match, still felt they could take much from the performance.
Defender Angel Rangel said: "It is disappointing, we played very well.
"It is difficult to come to this place and we know we didn't get a lot of the ball in the last three games we have had here - but we came here with so much confidence and we showed that.
"We scored early
Maybe that was a problem because we tried to defend with so many minutes ahead of us.
"It was always difficult because they have so many good players and in the end they were too good for us, but we fought all the way
We worked hard and were organised, apart from the goals.
"It is disappointing but there are a lot of positives."
City supporters are being urged by fellow fans to repeat their recent protest against UEFA prior to the Bayern clash.
Fans turned their backs and booed during the Champions League anthem ahead of the home game with CSKA Moscow on November 5
This was over perceived mistreatment by the European governing body for the October meeting between the two sides in Moscow, which was ordered to be played behind closed doors after a number of City fans had made travel arrangements.
They will be backed by some Bayern fans, who had a similar experience in the Russian capital in September.
A statement from the 1894 Group read: "We have heard little in the way of understanding towards supporters from UEFA after fans were denied access to the matches in Moscow."
Source : PA
Source: PA