Burnley have now dropped out of the top flight three times in five seasons. They will play in the Championship next season.
Erling Haaland scored the only goal early in the game. Jérémy Doku set him up with a precise pass. Haaland chipped the ball over Martin Dúbravka to give City the lead.
City created several chances after the goal. However, they failed to add a second. Manager Pep Guardiola showed frustration on the touchline as his team slowed the tempo.
Burnley nearly equalised before half-time. Zian Flemming missed a clear chance. Earlier, Dúbravka made a strong save to deny Rayan Cherki.
The win puts City level on points with Arsenal. They lead the table on goals scored. Both teams still have five matches to play.
City want a seventh league title in nine years. However, they face a tougher run-in than Arsenal. Their narrow win keeps the title race open.
Scott Parker has struggled to lift Burnley this season. The team has only 20 points from 34 matches. They sit 13 points from safety with four games left.
Burnley continue to move between the top two divisions. They have either gone up or down in each of the last five seasons.
Bournemouth drew 2–2 with Leeds United in another key match.
Junior Kroupi scored early for Bournemouth. An own goal by James Hill brought Leeds level. Bournemouth regained the lead before Sean Longstaff scored a late equaliser.
The draw moves Bournemouth into seventh place, above Chelsea. Leeds now sit nine points clear of the relegation zone.
