Watkins scored in the 73rd minute and Malen six minutes later after both came on midway through the second half to help lift Villa to fifth in the standings.
McGinn added the third as he followed up to convert the rebound after Aaron Ramsdale saved Marco Asensio’s stoppage-time penalty.
Ramsdale also stopped an earlier Asensio spotkick.
It was Southampton’s 13th home defeat of the season, setting a club record as they played for the first time since Monday’s sacking of manager Ivan Juric.
Villa, who host Paris St-Germain in the return leg of their Champions League quarterfinal on Tuesday trailing 3-1, saw Asensio’s 69th-minute penalty saved.
However, Watkins stretched out his right foot to guide a precise long-range pass from Youri Tielemans into the net off the underside of the bar for the opening goal.
“I think that’s a very important goal for a start,” Watkins told reporters.
“Sometimes you need that bit of luck and a bit of magic. It was nice to see that one go in and that’s one of my favourites to be honest.”
Watkins made an immediate impact after coming on as he won a penalty when brought down by Jan Bednarek but Asensio’s left-foot effort was expertly saved by Ramsdale’s one-handed stop.
“It was about being patient and once we got that first one the chances started coming more frequently,” added Watkins, whose opener was quickly followed by a thrashing shot from Malen to double the lead.
Home captain Jack Stephens brought down McGinn four minutes into stoppage-time, giving Asensio the chance to atone but Ramsdale saved again only for McGinn to bundle home the rebound.
Southampton, whose return to the Championship was confirmed last week with seven matches remaining, had the game’s first effort when Cameron Archer tested Villa keeper Emiliano Martinez in the 15th minute but the hosts offered little else in attack as they concentrated on defensive discipline in the first half.
After the break, Villa applied more of an attacking squeeze to earn the win and a boost ahead of their Champions League tie.
Southampton remain on 10 points with two league wins and still need two points from their remaining six matches to eclipse Derby’s record low haul of 11 points in the 2007-08 Premier League season.