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The Rams have still not scored away from home this season and are in desperate trouble.
But Villa made hard work of their task before two goals in the space of five minutes early in the second half earned them their second win in five outings.
But there were still question marks about their win carved out by goals from the ever improving Martin Laursen and Ashley Young.
Their midfield lacks driving force and, with skipper Gareth Barry not hitting the high spots, it enabled Derby to stay in contention until they were exposed by two strikes when Villa took advantage of some deplorable defensive play.
But the story might well have been different as there was very nearly a shock start when Steve Howard attempted a speculative long-range effort which Scott Carson flicked over the bar.
It was the only time Howard was really in with a chance of scoring as the Rams lacked any penetration to upset Villa's defence.
A couple of minutes later, Stephen Bywater was somewhat fortunate to keep out a Zat Knight shot from close range.
Bywater knew very little about what happened as the ball hit his outstretched arm and bounced away for a corner.
The pace of Villa's young attacking trio of Young, Luke Moore and Gabby Agbonlahor failed to upset Derby.
Darren Moore had been expected to struggle but in fact coped extremely well when he was aided by the agility of Dean Leacock.
Although Villa dominated long spells, they became increasingly frustrated by their inability to break down Derby's leaky defence.
Skipper Barry was strangely not so powerful as usual, while the return after suspension of Nigel Reo-Coker also failed to ignite the midfield where Stiliyan Petrov was again a major disappointment.
The longer the game progressed the more Derby appeared to rely on their blanket defensive coverage to foil Villa.
Villa's best clear-cut chance to break the stalemate in the first half occurred when Agbonlahor turned the slow moving Darren Moore to shoot on the turn only to see his effort wobble agonisingly just wide of the far post.
Young, who had been superbly contained by Andy Griffin, suddenly discovered his flair in the second period and opened the door for a Villa win.
It was Young who provided the free-kick from which Barry headed across an unmarked goal for Laursen to notch his third strike of the season in the 57th minute.
Five minutes later, Young scored himself after Jay McEveley lost possession to allow Agbonlahor to break through.
His shot bounced off Bywater into the path of Young to score his second goal of the campaign.