A draw would have flattered the Rams, who were desperately poor going forward and remain without am away goal this season.
However, Billy Davies' side did defend admirably, and goalkeeper Stephen Bywater was also in fine form when their backline was breached.
Bywater was lucky that Zat Knight fired straight at him from close range early on, but he made fine saves from Olof Mellberg's header and another Young free-kick to keep the game scoreless before the break.
Young, who gave Andy Griffin a torrid time on the left flank, was Villa's main threat in the first period and it was fitting that he was involved in his side's opening goal.
But it was not one that Davies will enjoy watching again as his defence stood stock still from Young's free-kick leaving Laursen to tap in unhindered after Barry headed the ball back across goal.
Four minutes later the game was all but over when Derby gave the ball to Gabriel Agbonlahor and, although Bywater saved his shot, Reo-Coker had the presence of mind to loop the ball back across goal to allow Young to slot home.
There was clearly no way back from that for the shot-shy Rams, although the introduction of Rob Earnshaw from the bench did at least increase their attacking threat.
Carson had been a spectator since making a fine stop from Howard in the opening minutes but he had to remain alert as the Welsh striker went close with two late efforts.
Villa, understandably, took their foot off the gas in the closing minutes but they had already showed that, even without injured targetman John Carew, they can break down the most stubborn of defences.
Aston Villa manager Martin O'Neill:
"The first half was very frustrating. We didn't play well enough, or get any momentum going.
"But we improved enough to win the game. We galvanised ourselves in the second half, got the breakthrough and went on to win it.
"We have been doing okay form-wise but this was a big win for us and it will give us a bit of confidence."
Derby boss Billy Davies:
"We could hear how frustrated their fans were getting and they knew how hard we worked and competed.
"For 45 minutes we did very well but two lapses of concentration at this level will always cost you.
"I was extremely disappointed with the manner in which they scored their first goal and we shot ourselves in the foot for their second too."
Aston Villa:
Carson, Mellberg, Knight (Davies 88), Bouma, Laursen, Young (Maloney 69), Petrov, Reo-Coker, Barry, Moore (Berger 77), Agbonlahor.
Subs Not Used: Taylor, Gardner.
Goals:
Laursen 57, Young 61.
Derby:
Bywater, Griffin, Moore, Davis (Teale 46), McEveley, Fagan (Earnshaw 66), Oakley, Leacock, Pearson, Barnes, Howard.
Subs Not Used: Price, Jones, Mears.
Booked:
Griffin, Moore, Howard.
Att:
40,938
Ref:
Mark Halsey (Lancashire).
