
City move up to fourth with 58 points from their 33 matches, four points ahead of both sixth-placed Chelsea and Aston Villa seventh, but they have played a game more.
The top five qualify for the Champions League next season.
O’Reilly stabbed the ball into the net from four metres after connecting with Matheus Nunes’s low cross, before Kovacic drilled in the second goal from the edge of the box to make sure of the win.
It was hard work for City for 85 minutes as they battled to create clear-cut chances, while James Tarkowski struck the post with a header from a corner in the first half for Everton, who remain in 13th place with 38 points from 33 games.