Aleksander Mitrovic’s goal, following a mistake by Tyrone Mings, looked set to condemn Villa to a second straight home defeat.
But Trezeguet came off the bench to net a quickfire double and Ollie Watkins also scored as Smith’s men came from behind to win for the first time in the Premier League this season.
Villa had struggled in attack before the boss brought Trezeguet, Keinan Davis and Jacob Ramsey off the bench.
He said: “Sometimes you need the impact to come from the subs bench and that is what happened.
“All three who came on made an impact on the game and lifted our performance. It changed the game for us.
“Trezeguet has come on and done what was asked of him. He has been a bit unfortunate this season and I’m really pleased for him.”
Villa were again without Jack Grealish after Smith revealed the skipper, who had been set to make a comeback after six matches out, complained of discomfort in training on Saturday.
“Jack wants to play more than anyone but when he tells you he has a little bit of pain still you have to take notice,” said Smith.
“We erred on the side of caution. Yes he is going to be a miss because of the things he brings to the team but the players have shown today they can go and get without him as well.
“We believe we have a quality squad. It is just about showing it on the pitch.”