Leon Bailey and Emi Buendia struck early in either half as Villa bounced back from a shock FA Cup exit to League Two Stevenage last weekend.
Patrick Bamford pulled a goal back for Leeds seven minutes from time, but defeat leaves Jesse Marsch's men still just two points above the relegation zone.
The visitors were left to rue a host of wasted chances, the first of which led to the opening goal as Marc Roca failed to connect when unmarked from a corner.
Villa rapidly broke clear on the counter-attack and Boubacar Kamara teed up Bailey to curl into the top corner after just three minutes.
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