Trezeguet's double boosted Aston Villa's hopes for survival as they won for the first time since January, beating Crystal Palace 2-0 at Villa Park.
Palace thought they had taken the lead through Mamadou Sakho early on, but VAR ruled the strike out for a handball, before Trezeguet put Villa ahead in first-half stoppage time with a finish at the far post (45+5).
Villa impressed in the second half and doubled their lead through the Egyptian again, poking under Vicente Guaita (59) from eight yards, and they held on with Palace offering very little in the final third as they stumble towards the end of the season.
To make matters worse for Palace, former Villa man Christian Benteke was sent off after full-time for an off-the-ball incident with Ezri Konsa.
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The result means Villa are four points from safety with three games remaining, but with a vastly inferior goal difference to both 16th-placed West Ham and Watford in 17th. Palace, who have now lost five on the bounce, are in 14th.
Aston Villa: Reina (6), Elmohamady (7), Konsa (7), Mings (7), Taylor (5), Hourihane (7), McGinn (6), Luiz (7), Trezeguet (8), Grealish (7), Samatta (6)
Subs: Targett (6), Nakamba (NA), Davis (NA), El-Ghazi (NA)
Crystal Palace: Guaita (7), Ward (5), Dann (5), Sakho (5), Van Aanholt (6), Kouyate (5), Milivojevic (5), McArthur (5), Zaha (5), Benteke (4), Ayew (5)
Subs: McCarthy (5), Townsend (5), Riedewald (5), Meyer (5)
Man of the match: Trezeguet
How Villa overcame tepid Palace for vital win
VAR was dominating again as early as the seventh minute as Sakho touched home Luka Milivojevic's free-kick ahead of Pepe Reina, with the Stockley Park officials ruling it had hit the defender's arm, though Palace will claim it hit his shoulder.
Villa were dealt a blow just before kick-off as the injured Kortney Hause was replaced by Ahmed Elmohamady, but the Egyptian nearly set up the opener as his fine cross was headed over by Mbwana Samatta in space.
Both goalkeepers were busy as Guaita stopped Jack Grealish's volley from another good Elmohamady cross, before Reina denied former Villa man Christian Benteke with a low block at the other end.
But deep into the lengthy stoppage time added on for the VAR review, Villa took the lead. Conor Hourihane's dangerous free-kick from the left was only half-cleared by Joel Ward, and Trezeguet arrived at the back post to control his effort beyond Guaita from close range.
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Villa continued to press after the break, and thought they had a penalty as Grealish went down near Patrick van Aanholt's challenge, but again VAR intervened, with replays showing the Villa man had actually initiated contact.
The goal was coming - Hourihane's free-kick was tipped wide by Guaita, before Konsa's point-blank touch was again cleared off the line by the goalkeeper before Villa's second - and it came again through Trezeguet. John McGinn's cross for Grealish was cleared as far as Hourihane, the midfielder's header back into the box found Trezeguet unmarked, and his first touch on the stretch allowed him to poke under Guaita with his second.
Van Aanholt nearly halved the deficit, Reina blocking his low shot well with 15 minutes remaining, but Villa came closest to getting the game's third goal, as Trezeguet and Davis both came within inches of latching onto Matt Targett's left-wing delivery.
Villa made just one change as Hourihane replaced El Ghazi following the 3-0 defeat by Manchester United.
Palace also made just one change following the 3-2 defeat by Chelsea as Sakho replaced the injured Cahill.
And Palace's day got even worse after full-time as Benteke was sent off by Martin Atkinson for an incident with Villa defender Konsa.
Villa have lost more points from winning positions than any other Premier League team, but were able to see the game out for a much-needed win to give them a glimmer of hope, while Roy Hodgson will be worried as five straight defeats sees Palace crawl towards the finish line.
What the managers said...
Villa boss Dean Smith: "It's felt a while since I had a big smile! It's really big. It's the first leg of a semi-final, and we've managed to win that, and we've got a second leg at Everton. It was a good performance and I think we deserved it today; we were worthy winners.
"It was a more attacking line-up today; we felt we'd have a lot more of the ball than we have against Liverpool and Man Utd, and it paid dividends.
"It gives everybody a big lift. Our performance since lockdown has been really good, that's our second clean sheet, defensively we've been better, and now we've scored some goals, which we needed to do, and created some chances."
Palace boss Roy Hodgson: "We put ourselves on the back foot going into half time. When the second goal went in we gave ourselves a mountain to climb, and quite frankly I never thought we looked like climbing that mountain today.
On Benteke's red card: "It's inexcusable, basically, that's the bottom line. There was a lot of niggling going on on the field, we're close enough to be aware of that, but the thing is that is part and parcel of the game we play, it is quite often present in a lot of football matches.
"And you must not allow it to provoke you into doing something that is going to stop you playing for the rest of the season. Christian Benteke just came back into the team, is playing his fifth or sixth game in a row, which of course he wasn't doing before football was halted, and it was a great opportunity for him to finish the season by getting these games under his belt, and now he's going to miss them.
"He's unhappy about that, of course, as we are, but unfortunately I can't excuse it, no matter how provoked he may have been, no matter what might have been said. You know that when you kick out at an opponent, and the referee sees it, you get sent off. That has been happening in football for as long as I can remember. All Christian can do, I guess, is apologise to his team-mates and accept his punishment."
- Aston Villa have now won a league game on all seven days of the week this season - becoming only the second side to achieve this in an English top-flight campaign after Tottenham Hotspur in 1986-87.
- This victory ended a 10-match winless streak for Aston Villa in the Premier League (D2 L8), with this their first win in the division since January versus Watford.
- Aston Villa scored as many goals in this win as they had across their previous eight league matches combined beforehand (two).
Villa now go to Everton on Thursday at 6pm, live on Sky Sports, before hosting Arsenal on July 21, also live on Sky Sports at 8.15pm. They finish the season at West Ham on July 26.
Palace host Manchester United at 8.15pm on Thursday, before going to Wolves on July 20, and hosting Tottenham on the final day of the Premier League season on July 26.