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Rob Hulse and Kris Commons scored twice in the space of three minutes and Derby should have had more goals before the visitors had the chance to regroup during the interval.
Michael Doyle reduced the arrears early in the second half and Derby's poise drained away, but they still had enough to deliver manager Nigel Clough's first victory in his fifth game in charge.
Coventry lost centre-half Ben Turner with a migraine before kick-off but that could not excuse a wretched first-half performance.
Hulse could have scored twice in the first five minutes, but Coventry's creaking defence finally folded in the 14th minute when goalkeeper Keiren Westwood could only push a Gary Teale corner across his goal and Hulse headed in at the back post.
Derby increased their lead two minutes later when Teale fizzed in a low cross and Hulse laid it back to Commons, who side-footed past Westwood from ten yards.
Commons should have scored again three minutes later when he was put clear by Nacer Barazite, but Westwood saved to his right and both Teale and Commons struck the woodwork before the interval.
Coventry could only improve and the introduction of Leon McKenzie for Freddy Eastwood along with the withdrawal of Derby centre-back Miles Addison gave them a foothold in the match.
Doyle scored in the 52nd minute when Clinton Morrison pulled the ball back across goal from the right and it needed an excellent saving tackle by Teale to deny Jordan Henderson an equaliser.
Derby began to wobble but Coventry could not conjure up another clear opening and Clough's team held on for the win that lifts them out of the bottom three.