The breakthrough took a while, but Villa ran out deserved winners against the struggling Rams.
Second-half goals from Martin Laursen and Ashley Young did the damage to send Villa into next week's Second City clash in good spirits.
And the winning margin could have been greater as Villa dominated for long periods.
Carson tipped a rising effort over the bar on two as Howard tried his luck from distance with a rising drive.
Knight saw a goalbound effort blocked by Bywater a minute later as Villa also had an early penalty appeal ignored when McEveley appeared to handle.
Fagan fired over the bar on seven as the early pace showed no sign of slackening.
Petrov sent a wayward shot wide of the target as he turned into space on 11.
Barry's shot on the run was deflected behind a minute later after Agbonlahor pounced on a weak clearance from Davis.
Moore fired narrowly wide with the outside of his right foot as he met Barry's cut back on the edge of the box on 20.
Agbonlahor went even closer moments later, sending a low shot on the turn just inches past the upright.
Young then saw a rising drive blocked as Villa started to turn the screw.
Mellberg was denied by Bywater on 22 as he rose to head a Barry corner goalwards.
Agbonlahor produced a turbo-powered run through the Derby defence on 26, but was denied by Griffin's sliding challenge just as he was about to shoot.
Young fired into the side netting as he cut in from the left on 32. Agbonlahor fired narrowly wide from an acute angle moments later.
Young's dangerous whipped free-kick from the left was scrambled away on 40.
Bywater parried another Young free-kick a minute later before Griffin completed the clearance.
Villa enjoyed plenty of possession at the start of the second-half, without really testing Bywater.
The Derby keeper did race off his line to beat Moore to a Barry through ball on 54.
Villa had the lead on 57 as Barry headed Young's free-kick from the left back across goal and Laursen hammered home from close range.
It was 2-0 on 61 as Bywater denied Agbonlahor, but Young fired into the roof of the net from the rebound.
Petrov's low drive was blocked on 67 as Villa pushed for a third.
Earnshaw might have reduced the arrears for Derby on 74, but fired narrowly wide as he found space behind Laursen.
Howard then headed over the bar as he met a corner from the right.
Maloney almost added a third for Villa on 79, but how low left-foot drive from the edge of the box flew inches past the post.
Agbonlahor cut in from the left three minutes later, but saw his low shot saved by Bywater.
VILLA: Carson, Mellberg, Bouma, Knight, Laursen, Petrov, Reo-Coker, Barry, Young, Moore, Agbonlahor. Subs: Taylor, Davies (for Knight 88), Berger (for Moore 78), Gardner, Maloney (for Young 69).
Derby: Bywater, McEveley, Leacock, Oakley, Howard (booked 87), Fagan, Griffin (booked 43), Davis, Moore (booked 46), Pearson, Barnes. Subs: Price, Jones, Earnshaw (for Fagan 66), Teale (for Davis ht), Mears.



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