The visitors impressed in a dominant opening 45 minutes as Matheus Cunha pounced on a Villa mistake to fire Wolves ahead.
But the hosts put on the pressure in the second half, which eventually paid off with a 73rd minute Watkins equaliser.
Wolves were defending deep and struggling for an outlet, as Ezri Konsa slid home the late winner.
But that misery was compounded in the 94th minute when Jhon Duran tapped home a third, meaning Wolves are now winless in five Premier League games this season.