Dean Smith’s side kicked off at Villa Park languishing seven points from safety, but Egypt winger Trezeguet scored twice to keep them in with a chance of avoiding relegation.
Villa’s first win in 11 league games lifted them into 18th place, within four points of fourth-from-bottom Watford with three games left.
Second-bottom Bournemouth will go one point above Villa if they beat Leicester later on Sunday.
Villa face Everton, Arsenal and West Ham in their last three matches as they battle to avoid an immediate return to the Championship.
Smith’s men got an early stroke of luck when Palace defender Mamadou Sakho had a goal ruled out by VAR.
Sakho got on the end of Luka Milivojevic’s free-kick but a check revealed the ball had gone into the net off the arm of the Palace defender.
Villa snatched the lead four minutes into first-half stoppage time.
Conor Hourihane’s free-kick from the left evaded everyone and Trezeguet came in at the back post to side-foot beyond Vicente Guaita.
It was Palace’s turn to be saved by VAR early in the second half.
Referee Martin Atkinson pointed to the spot after Jack Grealish appeared to be fouled by Patrick Van Aanholt, but a further check overturned the decision.
Villa got their crucial second goal in the 58th minute.
Hourihane nodded the ball forward after John McGinn’s cross was only half cleared and Trezeguet was on hand to slot home.
Palace striker Christian Benteke was sent off for violent conduct after the final whistle.
– Wolves in Champions League hunt –
At Molineux, Raul Jimenez’s penalty and Leander Dendoncker’s header a minute either side of half-time put the game out of Everton’s reach.
Diogo Jota beat Jordan Pickford at his near post 16 minutes from time to round off another performance that will see the England number one scrutinised.
Victory lifts Nuno Espirito Santo’s Wolves back ahead of Sheffield United into sixth and within four points of fourth-placed Leicester.
Fifth could also be good enough for the riches of Champions League football next season should Manchester City’s appeal against a two-season ban from European competitions fail when the Court of Arbitration for Sport’s verdict is revealed on Monday.
Should Wolves win their next two games against Burnley and Crystal Palace, they could have the chance to snatch Champions League football from Chelsea when they visit Stamford Bridge on the final day of the season.
Goals have been hard to come by for Nuno Espirito Santo’s men since the season’s restart last month with just four in their previous five games.
But they were given a helping hand by an Everton side meandering towards the end of the campaign with little purpose.
Daniel Podence lured Lucas Digne into committing a penalty in first half stoppage time and Jimenez coolly sent Pickford the wrong way for his 25th goal of the season.
Dendoncker doubled the hosts advantage early in the second half as he flicked Pedro Neto’s in-swinging free-kick into the far corner.
Pickford has made a string of eye-catching errors since the Premier League’s return and was inches away from conceding an embarrassing third as Podence’s shot squirmed between his legs before he just recovered in time to prevent the ball going over the line.
Burnley’s Nick Pope shone in a 1-1 draw at Anfield on Saturday to end Liverpool’s perfect home record in the Premier League this season to further his case for ousting Pickford at international level.
And the Everton stopper did his case little favours when Wolves’ third goal did arrive as Jota controlled Ruben Neves’s great long pass over the top before firing in at the near post from a narrow angle.
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