The Sky Blues went in front after 27 minutes as Joel Latibeaudiere headed home Josh Eccles' corner at the near post.
Although both sides had chances in the second half, the hosts cashed in when Connolly nodded home Josh Morton's cross to keep Hull's unbeaten run intact.
Liam Rosenior's men are up to fifth in the EFL Championship table while Coventry sits 11th following a fourth consecutive draw.
Story of the match
Before the match, there was a moment of silence to remember the victims of the natural disasters in Morocco and Libya.
Once the action got underway, there were a limited amount of chances although Hull had the first opportunity as Scott Twine sent the ball across the face of goal only to see it go behind for a goal kick.
Jean-Michael Seri's shot was deflected behind for a corner and from the resulting corner, Lewie Coyle found Connolly but his volley at the back post was wide.
On 25 minutes some neat passing by Coventry saw Jay Dasilva find some space only to shoot narrowly past the left post.
Moments later, the Sky Blues were in front. Latibeaudiere met Yasin Ayari's delivery to head past Ingram and into the bottom corner, his first goal for the club.
It should have been two as after an excellent pull-back by Matty Godden, Ayari spotted Haji Wright in the six-yard box but he couldn't keep his shot down.
Delap then had his effort deflected after creating for himself with a cheeky flick, Jacob Greaves won the first header from Twine's corner and Connolly fired wide from close range.
In the second half, the lively Twine tested Wilson from distance but he pushed the shot away and at the other end, Eccles' long-range strike went wide.
Ingram came up big, parrying from Liam Kelly and Cyrus Christie denied Godden as the visitors looked to stretch their advantage.
Jaden Philogene then curled one that went out wide off of Kyle McFadzean, Twine also went wide from the resulting corner and Wilson held his next attempt.
Christie was next to try his luck but the ex-Coventry man failed to hit the target and his low cross was sent across goal and substitute Tyler Morton struck wide from distance.
The hosts continued to push for an equalizer, Coyle's cross-shot stopped by Wilson and he saved with his feet from Twine's close-range shot.
Late on, Jason Lokilo's free-kick struck the Sky Blues' wall before the hosts finally made all their pressure pay off as the corner was cleared away but Morton's pass into the box was flicked home by Connolly with his head.
Man of the match: Jacob Greaves
Had a massive night in the Hull defense, making a vital block early on then clearing the subsequent corner.