Alexis Sanchez celebrates with Olivier Giroud and Theo Walcott after scoring the second goal for Arsenal. PHOTO: REUTERS
In his final home game as City manager before handing over to Pep Guardiola, Manuel Pellegrini saw Kevin De Bruyne put the hosts in front after Sergio Aguero's early opener was cancelled out by Olivier Giroud.
But Sanchez's strike means that Pellegrini is now dependent on fifth-place Manchester United dropping points in their last two games -- or Arsenal losing at home to Aston Villa -- if his side are to finish in the top four.
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Having seen his team tamely concede defeat against Real Madrid in the Champions League semi-finals on Wednesday, it threatens to be a miserable end to Pellegrini's three-year tenure, which has yielded the 2013-14 Premier League title and two League Cups.
United visit West Ham United on Tuesday before finishing the season at home to Bournemouth and if they win both games, and Arsenal avoid defeat against bottom club Villa, Guardiola will begin life at City as a Europa League manager.
For Arsenal, victory over Villa in next Sunday's final game will secure a Champions League berth for the 19th season running and they could yet finish above local rivals Tottenham Hotspur, who they trail by two points.
But there was a concern for Arsenal manager Arsene Wenger, and his England counterpart Roy Hodgson, in the shape of a first-half injury to Danny Welbeck.
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The match programme contained a message from Emirati club chairman Khaldoon Al Mubarak thanking Pellegrini and hailing his "engaging approach, integrity and humility".
In his own notes, Pellegrini describing managing City as a "privilege" and said that he would "take nothing but great memories" to his next job.
City failed to register a single shot on target in their meek 1-0 Champions League semi-final defeat at Real Madrid, but after a sprightly start they went ahead in the eighth minute.
Jesus Navas's cross from the right was nodded back and down by Fernandinho and Aguero eluded Mohamed Elneny before driving a left-foot shot into Petr Cech's bottom-left corner.
Arsenal had barely set foot in City's half, but within two minutes their former player Gael Clichy offered them an attacking foothold with a misjudged back header that bobbled past a scrambling Joe Hart, hit the post and went behind for a corner.
Eliaquim Mangala, deputising for injured skipper Vincent Kompany, misjudged Elneny's delivery and Giroud headed home his first goal in 16 league outings.
Arsenal were quickly deflated again, however, as an apparent knee injury to Welbeck saw the England forward walk straight off the pitch and down the tunnel, with Jack Wilshere coming on and Alex Iwobi moving wide.
Arsenal were already missing German playmaker Mesut Ozil due to what the club said was a "slight hip injury".
After warning shots from Jesus Navas and Fernandinho, City went ahead in the 51st minute.
De Bruyne brought down a bouncing ball just inside the Arsenal half and held off Hector Bellerin before surging towards goal, cutting inside Elneny and guiding a low shot past Cech's outstretched right hand.
But the introduction of Theo Walcott for Iwobi provided an injection of dynamism to Arsenal's attack and after he had lofted a shot wide from Giroud's lay-off, the visitors equalised through Sanchez.
Picking the ball up deep, the Chilean forward rolled a pass forward to Giroud, who brilliantly steered it back into his path, and Sanchez powered through a gaping hole in the City defence to clip a shot past Hart.
Pellegrini sent for the cavalry, with Raheem Sterling, Yaya Toure and Wilfried Bony all joining the fray, but the closest his side came to a winner was a deft Bony volley that crashed against the bar.
Pellegrini, who bows out at Swansea City next Sunday, covered his face with his hands in anguish.
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