O’Reilly put City ahead in the first half at the Etihad Stadium and restored their lead after Lewis Hall had equalised.
Pep Guardiola’s side weren’t at their best, but they held on for a victory that moved them within two points of leaders Arsenal.
The Gunners travel to Tottenham on Sunday, but regardless of the result in the north London derby, City control the destiny of the title.
They will have a game in hand on Arsenal after this weekend and host Mikel Arteta’s men in April, with 11 wins from their last 11 matches guaranteed to secure the seventh title of Guardiola’s reign.
While Arsenal have spluttered with two wins from their last seven league games, City are heating up at just the right time.
A fifth successive win in all competitions extended their unbeaten run to eight games.
“We saw today this is how we need to play. It’s coming to the best part of the season. Every single game will be similar to today,” Guardiola said.
“Of course in terms of points it’s important, but we have to improve to have the chance to compete until the end. Now we deserve three more days off. Then another battle in Leeds.”
At Stamford Bridge, Chelsea climbed into the top four only on goal difference after they paid for failing to build on Joao Pedro’s fourth-minute opener.
Chelsea were dominant until Wesley Fofana was sent off with 18 minutes remaining for a second yellow card.
Burnley took full advantage as Zian Flemming headed in from a corner in the 93rd minute to boost their battle to beat the drop.
“It is not enough clean sheets and not enough basic values of defending set-pieces. That is something I have to address,” said Chelsea boss Liam Rosenior.
“There were players on the pitch who were assigned to do their job and who didn’t do their job. That is what cost us the two points.”
Aston Villa defied the odds to keep pace with Arsenal and Manchester City in the title race until recent weeks, but a 1-1 draw continued their poor run at Villa Park.
Anton Stach’s spectacular free-kick from fully 40 yards at an angle caught out Emi Martinez at his near post to give Leeds the advantage.
Daniel Farke’s men have lost just twice in their last 14 league games to relieve their fears of being dragged into a battle for safety.
But Tammy Abraham then snatched a point for Villa two minutes from time.
Five Premier League sides are set to qualify for next season’s Champions League thanks to the strong performance of English sides in European competition this season.
Liverpool and Manchester United have the chance to close in when they face Nottingham Forest and Everton in the coming days. (AFP)
Edited by Tony Sabine
