In the first-ever match between the two sides, Cody McDonald's early opener was cancelled out by a Richard Hinds header in a pulsating game at Huish Park.
The Sky Blues got off to a dream start after 10 minutes when a free-kick from former Rangers midfielder John Fleck was met by the head of McDonald, with the ball nestling in the top corner past Yeovil goalkeeper Marek Stech.
The home side bounced back from the early setback after 21 minutes as centre-back Hinds headed home an Ed Upson corner, scoring his third goal in two games.
Coventry should have retaken the lead before half-time when McDonald swooped on a Jamie McAllister error to go through on goal but fired straight at Stech.
Amid an evenly-contested second half, the hosts thought they had snatched a winner 10 minutes from time courtesy of Byron Webster's close-range effort, only to see it ruled out after the referee adjudged Hinds to have controlled using his arm.