Leon Bailey and Emi Buendía scored early in each half as Villa bounced back from a surprise FA Cup exit to League Two Stevenage last weekend.
Patrick Bamford scored for Leeds with seven minutes remaining, but defeat leaves Jesse Marsch’s men still just two points outside the relegation zone.
The visitors had to lament a host of wasted chances, the first of which led to the opening goal when Marc Roca missed to connect when he was open from a corner. Villa cleared quickly on the counter-attack and Boubacar Kamara helped Bailey curl up in the top corner after just three minutes.
Thereafter Leeds dominated the first half, but a combination of poor finishing, luck and the inspired form of Emiliano Martínez in the Villa goal kept them at bay. Rodrigo evaded World Cup winner Argentina, but his scoring effort was cleared off the line by Villa debutant Alex Moreno.
Jack Harrison looked sure to equalize when he stormed to meet Luke Ayling’s cross at the far post, only to be denied by an impressive reaction from Martinez. Rodrigo finally had the ball in the Villa goal in first-half stoppage time, but the Spaniard had drifted slightly offside in the build-up to the goal.
The pattern continued early in the second period, as more heroics from Martinez were needed to reverse a curling effort from the impressive Willy Gnonto. But Leeds took another punch when Illan Meslier could only parry Bailey’s powerful shot and Buendía headed the rebound past the French keeper.
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 scintillating display as the young Italy international showed his strength before powering past Bamford to score in his first appearance since October. But it was too little, too late for Leeds as their winless run stretched to seven games.
Villa remain in 11th place but move level on points with Chelsea as they move closer to the top half.