A brace for Coventry striker Patrick Suffo made it a miserable afternoon for new Derby chairman John Sleightholme, who was watching his first Rams game since fronting a £15m takeover of the club.
But he must have been questioning his consortium's investment after seeing George Burley's side comprehensively outplayed by the visitors.
Coventry started brightly and after Graham Barrett had come close, Stephen Warnock put them ahead on ten minutes following a mistake by Dave Walton.
Full back Andrew Whing swung a deep cross into the home box which Walton completely misjudged and Warnock made no mistake with a half-volley from eight yards.
The goal sparked Derby into life and Daniele Dichio flashed a header wide before seeing another effort ruled out for offside.
But seven minutes before the break, Suffo doubled the Sky Blues' lead after another error in the Derby defence.
Andy Morrell fired a low centre across the face of goal and full-back Richard Jackson sent his attempt at clearance straight to Suffo who slotted home from 12 yards.
Burley responded by making a double substitution at half time, and eight minutes after the restart 16-year old midfielder Lee Holmes beat Pegguy Arphexad to put Derby back in the game.
However, the expected push for an equaliser never materialised and instead it was the visitors who continued to carry the greater threat.
Youssef Safri, Mo Konjic and Barrett all came close before Suffo sealed the points ten minutes from time when he dispossessed Michael Johnson and beat Lee Grant from a tight angle.
After the game, Derby boss Burley said: "We shot ourselves in the foot at the back today. We conceded three very bad goals and didn't really start playing at all.
"All credit to Coventry because they created plenty of chances but I'm very disappointed with our performance."
Derby: Grant, Jackson, Walton, Johnson, Zavagno, Costa, Valakari, Huddlestone, Holmes, Dichio, Morris. Subs: Camp, Mills, Bolder, Boertien, Svensson.
Coventry: Arphexad, Whing, Shaw, Konjic, Warnock, Barrett, Safri, Staunton, Doyle, Morrell, Suffo. Subs: Shearer, Pead, Adebola, Davenport, Mansouri.
Referee: R Pearson (Co Durham).