The home side had the game won inside the first half and, although the visitors did come back after the break, they never really possessed enough striking threat to make a comeback likely.
Coventry started brightly and carved out a couple of early chances. Dele Adebola produced a clever back-heel for Stephen Hughes whose shot went wide of the Hull goal.
Then, after seven minutes, the lively Jay Tabb had a sight of goal but his shot flew over the bar.
At the other end Hull were looking lively without really creating much of any note, although Coventry keeper Andy Marshall had to leave his line in a rush to deny Nicky Forster.
The game was becoming scrappier and scrappier and was badly in need of a goal.
It came at just the right time - but Hull were not happy at referee Tanner's decision.
They could hardly argue that David Livermore had not fouled Hughes but they clearly thought the offence had happened outside the area.
Their protests came to nothing and Michael Doyle slotted his third goal of the season with impressive cool.
Tabb was causing the visitors all sorts of problems down the left. Just short of the half-hour mark he beat Sam Ricketts and delivered a fine cross which Danny Coles had to head over from the goal-line.
Hull had not recovered from the first goal when they found themselves two down. They gave the ball away by their own corner flag, and when Isaac Osbourne swung in a cross, McKenzie was left unmarked and headed in from close range.
Livermore tried his best to pull his side back into the game when he fired just over before the break, but Hull never looked a real force.
The game was even scrappier after the break and Ian Ashbee went into the book for a foul on Doyle, soon to be followed by Forster for dissent.
The former Reading and Brentford man had a chance to bring his side back into the reckoning when, in the 63rd minute, he sprinted clear, only to drag his shot wide of goal.
Coventry had taken their foot off the pedal and really could have paid the price.
Only a very good save from Andy Marshall kept Dean Windass at bay in the 70th minute when the veteran looked set to score with a close-range header.
Still the home side continued to drop too deep, and when they did manage to get the ball forward, it came back far too quickly allowing Hull to rebuild.