Dean Smith’s men had looked destined for their second straight home defeat when Aleksander Mitrovic pounced a Tyrone Mings error to put the visitors ahead.
But substitute Trezeguet sparked a remarkable turnaround by scoring twice in quick succession.
Ollie Watkins then ended his own two-month Premier League goal drought to seal the points.
This was the first time Villa had come from behind to claim victory this season and the manner of it was made even more remarkable by the fact they had failed to register an attempt on target for the opening 75 minutes.
Once again missing Jack Grealish, who wasn’t risked after feeling discomfort in his shin during training on Saturday, they looked set for another frustrating afternoon when Mings underhit a backpass, allowing Mitrovic to open the scoring just past the hour mark.
But the England international then redeemed himself by delivering the cross from which Trezeguet equalised with his first goal of the season.
Four minutes later his second arrived when he converted a cross from fellow substitute Keinan Davis. When Watkins then netted, Villa had scored as many goals in the space of 10 minutes as in their previous six matches combined.
The win was Villa's first for five matches and moved them back up to ninth in the table. They cannot, just yet, be ruled out of the race for European football. Fulham, who would have climbed out of the relegation zone with victory, remain in the bottom three.
With Grealish still out, the only change from the team beaten 2-0 by Tottenham prior to the international break saw Anwar El Ghazi replace Trezeguet on the wing.
Fulham handed Mitrovic a rare start and the Serbia international was quickly into the action, drawing two saves from Villa goalkeeper Emiliano Martinez inside the opening 10 minutes, the second a curling effort tipped round the post.
Mitrovic also saw appeals for a penalty waved away as he tangled with home defender Tyrone Mings, while the visitors bright start continued when Bobby De Cordova-Reid headed wide of the target.
John McGinn was Villa’s liveliest player in the early stages, the Scotland international shooting over the bar from just outside the box after a bustling run forward.
The home side were pressing high up the pitch and giving the visitors little time on the ball. But their work in the final third lacked finesse, Douglas Luiz wasting a good chance when he headed Matty Cash’s cross wide of the target.
On the stroke of half-time came controversy as Villa were awarded a penalty before then seeing referee Andy Madley change his mind.
The official first waved away appeals when McGinn tumbled in the box but seconds later did point to the spot when Watkins went down after appearing to be clipped by Mario Lemina.
But Madley overturned his decision after consulting the pitchside monitor, ruling the Fulham man had made sufficient contact with the ball.
It meant Villa ended the half without having tested visiting goalkeeper Alphonse Areola.
The second half began in similarly frustrating fashion with El Ghazi seeing an effort blocked. At the other end, De Cordova-Reid drove straight at Martinez from outside the box.
In truth it was difficult to see where a goal was coming from for either team before, just as they had done last time out against Tottenham, Villa gifted their opponents the lead.
Mings sliced his intended backpass straight into the path of Mitrovic, who skipped round Martinez before slotting the ball into the net.
It took until 15 minutes from time for Villa to bring the first save of the match from Areola and even then he comfortably held Bertrand Traore’s long range drive.
But the home side’s second attempt on target brought them level, Trezeguet firing home Mings’ low cross.
Four minutes later the turnaround was complete, Davis doing brilliantly to rob Tosin Adarabioyo before racing into the box and delivering a cross which Trezeguet hammered past Areola.
With three minutes remaining Watkins made the game safe, finishing from close range after excellent work by Traore.
Villa (4-3-3): Martinez, Cash, Konsa, Mings, Targett, McGinn, Luiz (Ramsey 74), Sanson (Davis 67), Traore, Watkins, El Ghazi (Trezeguet 62) Subs not used: Elmohamady, Engels, Taylor, Nakamba, Barkley, Heaton (gk).
Fulham (4-4-1-1): Areola, Tete, Andersen, Adarabioyo, Aina, Cordova-Reid, Lemina, Reed, Lookman (Cavaleiro 47), Loftus-Cheek, Mitrovic Subs not used: Ream, Bryan, Onomah, Maja, Anguissa, Kongolo, Robinson, Fabri (gk).