The defeat confirmed the Clarets’ third Premier League relegation in five seasons, consigning them to the Championship alongside Wolves next season.
Erling Haaland scored the only goal as Pep Guardiola’s men ended the day top of the table for the first time since August, but the City boss was frustrated at his side’s inability to win by a greater margin.
City go ahead of the Gunners only on goals scored, with five games left for both the title contenders.
“The chances were there. We created a lot. We made a fantastic game,” said Guardiola. “We did everything after a demanding game three days ago.”
However, City have on paper the tougher run-in as they aim to snatch a seventh league title in nine years.
Fresh from beating Arsenal 2-1 in what was billed as a title decider on Sunday, the visitors roared out of the blocks.
A stunning save by Martin Dubravka turned Rayan Cherki’s shot onto the woodwork.
Haaland was then set free by Jeremy Doku and coolly chipped over the advancing Dubravka with just five minutes on the clock.
City continued to pepper Dubravka with efforts from distance, but Guardiola grew visibly angry as they let the tempo drop in their pursuit of more goals.
Burnley could even have been level by half-time as Zian Flemming dragged a glorious chance wide.
Haaland hit the post after the break, but City’s failure to rack up a more convincing scoreline leaves the title race tantalisingly poised.
At the other end of the table, Burnley have to rebuild once more in the second tier.
A return of just 20 points from 34 games has left Scott Parker’s men 13 adrift of safety with only four games remaining.
“We’ve fallen a bit short. The facts are we had to overachieve this year and we’ve not managed to do that,” said Parker.
“In certain moments we’ve lacked a certain quality about us and not managed to get enough points.”
It is the fifth consecutive season that Burnley have either been relegated or promoted as they oscillate between the riches of the Premier League and the Championship.
Three wins from their opening nine games offered hope that they could join Sunderland and Leeds in bucking the trend of promoted sides being immediately relegated back to the second tier.
However, just one win in their 25 matches since has sealed their fate.
Parker has become a Championship specialist, also winning promotion in the past with Fulham and Bournemouth.
But the former Tottenham and Chelsea midfielder has consistently struggled at all three clubs to make an impact in the Premier League.
Bournemouth’s challenge to qualify for Europe for the first time was dented by Sean Longstaff’s 97th-minute equaliser for Leeds in a 2-2 draw.
Junior Kroupi’s opener for Bournemouth was quickly cancelled out by a James Hill own goal.
Rayan’s strike had the Cherries on course for the top six until Longstaff’s volleyed leveller.
A point edges Bournemouth above Chelsea, who sacked Liam Rosenior on Wednesday, into seventh.
Leeds are now nine points clear of the relegation zone. (AFP)
