Dean Smith's side have their survival fate in their own hands after Trezeguet's first-half strike at Villa Park.
Villa seized their chance with a first home Premier League win over Arsenal in 18 attempts dating back to 1998.
Villa are now fourth bottom and have moved ahead of third bottom Watford on goal difference, with Smith's men on -26 compared to the Hornets' -27.
They head to West Ham for their final game of the season on Sunday, while Watford visit Arsenal and second-bottom Bournemouth, three points from safety, travel to Everton.
There are a multitude of permutations that could decide relegation, but Villa will be safe if they can better Watford's result on what is certain to be a dramatic finale.
If Villa and Watford both win, goal difference or goals scored will decide who goes down.