Olivier had two goals and an assist, and Coyle had a goal and two assists for the Blue Jackets (9-7-1). Adam Fantilli scored for the third straight game and Jet Greaves made 25 saves.
Kirill Marchenko had an assist to extend his point streak to 10 games (12 points; three goals, nine assists).
Leon Draisaitl scored twice, Evan Bouchard had three assists and Calvin Pickard made 20 saves for the Oilers (8-7-4).
Connor McDavid had two assists to extend his point streak to seven games (13 points; four goals, nine assists).
The Oilers won their previous two games in overtime – 5-4 at home against the Blue Jackets on Monday and 2-1 at the Philadelphia Flyers on Wednesday.
Olivier gave Columbus a 1-0 lead at 15:36 of the first period on a tip of Coyle’s shot.
Coyle scored 44 seconds into the second period to make it 2-0 after Olivier stole the puck from McDavid and fed him at the crease.
Matt Savoie cut it to 2-1 at 8:09, redirecting Bouchard’s shot, and Draisaitl tied it 2-2 at 9:49 with a one-timer from the right circle off a pass by Bouchard.
Denton Mateychuk made it 3-2 for the Blue Jackets at 10:19, scoring short side from the right circle off a rebound.
A goal by McDavid to make it 3-3 was overturned at 11:30 when the Blue Jackets successfully challenged that Draisaitl was offside.
Fantilli upped the score to 4-2 at 18:20, tucking in a loose rebound at the left post.
Olivier made it 5-2 at 7:30 of the third period, setting up in the slot and scoring off a pass from below the net from Coyle.
The Oilers pulled to within 5-3 at 7:57 on a goal by Vasily Podkolzin from the slot.
Draisaitl made it 5-4 at 11:27 with a wrist shot from the right circle.