The Robins took the lead in the 17th minute despite Coventry fans feeling their goalkeeper Keiren Westwood had been fouled in the lead up to the goal.
Michael McIndoe swung a high cross into the box from the left and Westwood was left on the ground as he challenged Adebola for the ball. Despite the best efforts of the Coventry defence, the big striker knocked the ball into the net.
After receiving treatment for three minutes, the Sky Blues' keeper was replaced by Andy Marshall.
Referee Phil Dowd then further enraged the home supporters when he refused to give Coventry a penalty after Bristol City defender Liam Fontaine pulled back Clinton Morrison inside the box.
The Staffordshire official then sent Coventry manager Chris Coleman to the stand after he made his feelings known about the decision.
Coventry had three chances to equalise in first-half stoppage time when keeper Adriano Basso saved efforts from Michael Mifsud and Morrison and the former Crystal Palace forward also hit the sidenetting.
The visitors doubled their advantage in the 54th minute when Adebola turned defender Scott Dann after receiving Bradley Orr's throw-in. The striker hit a pass to McIndoe and he cut in from the left to drill a low shot into the far corner.
Substitute Leon McKenzie wasted two great chances for Coventry and Morrison then saw Basso make a point-blank save from his close-range header.
Bristol City added a third goal in the 90th minute when substitutes Ivan Sproule and Steve Brooker combined for the latter to knock the ball home from ten yards.