Howard powered home his seventh of the season 14 minutes from time after Stern John had earlier cancelled out Jon Stead's opener.
Sky Blues manager Micky Adams axed Stephen Hughes from the first 16 for the first time this season after taking the captain's armband off him in midweek.
New skipper Robert Page and his team-mates should have been celebrating an early goal for the home team in the eighth minute.
Derby made Coventry pay heavily for the miss by taking the lead three minutes later.
Howard's flick-on fell to Stead and he turned Richard Duffy before firing a wonderful shot from 20 yards into the roof of the net for his first goal since joining the club on loan from Sunderland.
But Coventry supporters were cheering when their side drew level in the 22nd minute through John, who failed to score in his loan spell at Pride Park last season.
Clive Clarke's centre from the left was headed on by Elliott Ward and John reacted quickly to stab the ball in from seven yards.
Derby midfielder Seth Johnson was the first player to be booked for his foul on McKenzie in an open, entertaining game.
The impressive Giles Barnes went on a great run down the left and side-stepped Duffy to set up Stead but his close-range shot was blocked by Page.
After the break, Derby took greater control although there were still chances at both ends.
Then it was Stead who almost cracked in his second but his shot was turned away by Marshall in the Coventry goal.
Billy Davies made three substitutions in quick succession and the change worked for the visitors.
One of his subs, Ryan Smith, whipped in the corner which led to the winning goal. The cross was inch-perfect and Howard made the most of it.