Brighton created the better chances in a tightly-contested first period where clearcut opportunities were few and far between.
The contest appeared to be heading towards a goalless draw after both teams had goals ruled out for offside infringement.
However, Brighton were given the chance to claim all three points when Ezri Konsa was penalised for a foul on Simon Adingra in the box.
Pedro saw his spot kick saved, but he headed in from the rebound to end Brighton's six-game winless run and condemn Villa to a second straight defeat following Thursday's European loss to Olympiacos.
The Villans remain in fourth position and seven points clear of Tottenham Hotspur, who could close that gap in their away meeting with Liverpool.
VAR frustrations
Brighton carved out the first meaningful chance of the contest, with Adingra driving towards the edge of the box before forcing Robin Olsen to push the ball away from danger.
After Adingra saw his early effort saved, the two sides began to cancel one another, resulting in a cagey first period at the Amex Stadium.
However, Brighton threatened to break the deadlock in the closing stages of the first half when Pascal Gross latched onto Adingra's pass before being denied by Villa's deputising goalkeeper.
After going into the break on level terms, the visitors showed brief signs of improvement in the opening stages of the first half.
However, Brighton continued to offer the greater attacking threat, with Pedro drawing a strong stop from the Villa shot-stopper.
Moments later, Gross looked to have given the Seagulls the lead when he turned the ball in at the near post from Igor's low cross.
However, the midfielder's muted celebrations suggested that he may have been beyond the last man, and that theory was ultimately confirmed by the subsequent VAR review.
Villa then experienced their own disallowed goal after John McGinn had tucked the ball home from an offside position.
Pedro snatches maximum points
Despite putting the ball in the net, Unai Emery's side were off the boil and struggling to play the sort of football that has moved them into a top-four position.
Nevertheless, they still appeared to be on course to pick up a useful point after Danny Welbeck steered his header inches wide from Julio Enciso's cross.
However, there proved to be a moment of late drama when referee Rob Jones pointed to the spot for Konsa's foul on Adingra, who had been Brighton's standout player throughout the game.
After seeing his penalty saved by Olsen, Pedro pounced on the rebound to head the ball home and become the first Brighton player to find the net since Welbeck scored in March's 2-1 defeat to Liverpool.
The Seagulls have now taken their tally to 47 points, moving them into 11th place with just one point separating them from the top half of the table.
As for Villa, they will have to quickly pick themselves up for Thursday's trip to Greece, where they will attempt to overturn a 4-2 deficit in their Europa Conference League semi-final tie against Olympiacos.