By SABC Sport
30th December 2023
Villa led at the break thanks to a Moussa Diaby finish after Leon Bailey's 28th-minute opener for the hosts had been cancelled out three minutes later by Zeki Amdouni.
Burnley suffered a further setback with Sander Berge sent off early in the second half, but it looked as if it could prove a frustrating afternoon for Villa after Foster drew things level again in the 71st minute.
Luiz then had the final say, converting from the spot with a minute of normal time remaining, as Unai Emery's side moved up a place to second in the table, joining Liverpool on 42 points ahead of the Reds hosting Newcastle on New Year's Day.
The 26th league win of their superb 2023 under Emery saw the midlands outfit bounce back from the 3-2 Boxing Day loss at Manchester United, with normal service resumed at Villa Park after the 1-1 draw with Sheffield United on December 22 had ended a club-record run of 15 consecutive home league wins.
Vincent Kompany's Burnley, meanwhile, remain second-bottom, five points adrift of safety.
Villa had a couple of opportunities in the opening quarter-hour, with Diaby sending a volley wide and another from Ollie Watkins saved by James Trafford.
Burnley were then forced into an early change as Jordan Beyer was replaced by Hannes Delcroix, before starting to show some threat as Josh Brownhill struck wide and quickly brought a save out of Emiliano Martinez.
Within moments Villa were ahead, Watkins cutting into the box from the left and laying the ball to Bailey who took a touch and fired past Trafford via a deflection.
The lead proved short-lived, with Burnley hitting back almost immediately through Amdouni's hooked effort after Dara O'Shea had headed a free-kick across goal.
The visitors then had the ball in the net again in the 37th minute, but Foster's finish was ruled out for offside.
Villa regained the advantage five minutes later with Watkins again the creator, the England striker fashioning the cut-back from which Diaby turned the ball home.
Following Foster and Amdouni efforts saved by Martinez either side of the interval, Burnley were reduced to 10 men in the 56th minute when Berge collected a second yellow card having tugged at the shirt of Luiz.
Diaby curled over soon after before Foster prodded wide following a possible handball by Diego Carlos just outside the box that brought no action from referee Stuart Attwell.
Villa cranked up the pressure as Trafford denied John McGinn and Diaby before Luiz, Jacob Ramsey and Diaby, twice, shot off target.
The hosts were then left ruing that as Foster held off Alex Moreno and fired in for his first goal since returning to action after an eight-match absence in which he had been receiving care for his mental health.
It appeared as if Villa's wastefulness might cost them, but as stoppage time drew near a challenge by former Villa man Aaron Ramsey on fellow substitute Jhon Duran prompted Attwell to point to the spot and Luiz converted the penalty with a shot that bounced down off the bar to ensure a fine calendar year ended on a high for Emery's team.