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.
Thereafter, Leeds dominated the first half but a combination of poor finishing, fortune and the inspired form of Emiliano Martinez in the Villa goal kept them at bay. Rodrigo did evade the Argentine World Cup winner, but his goalbound effort was cleared off the line by Villa debutant Alex Moreno.
Jack Harrison seemed certain to equalise when he stormed in to meet Luke Ayling’s cross at the back post only to be denied by a stunning reaction save from Martinez. Rodrigo finally did have the ball in the Villa net in first-half stoppage time, but the Spaniard had strayed fractionally offside in the build-up to the goal.
The pattern continued early in the second period as more heroics were needed from Martinez to turn behind a curling effort from the impressive Willy Gnonto. But Leeds were hit with another sucker punch when Illan Meslier could only parry Bailey’s powerful drive and Buendia headed the rebound over the French goalkeeper.
Villa’s celebrations were initially cut short by the offside flag, but the goal was given after a VAR review. Gnonto finally had something to show for a brilliant display when the young Italian international showed his strength before teeing up Bamford to slam home on his first appearance since October. But it was too little, too late for Leeds as their winless run extended to seven games.
Villa stay in 11th but move level on points with Chelsea as they close in on the top half.