Striker Christian Benteke calmly slotted home an injury-time penalty for his first strike of 2015 after Baggies forward Saido Berahino had cancelled out Gabriel Agbonlahor’s opener, which ended the former England hitman’s 14-game goal drought.
Victory handed former Tottenham manager Tim Sherwood his first points as Villa boss, and saw the Villans move three points clear of the relegation zone and 18th-placed QPR.
Former Manchester City midfielder Jack Rodwell, meanwhile, cancelled out a first-half strike from Senegal frontman Dame N’Doye as Sunderland claimed a vital point at Hull City in a clash of two relegation-threatened sides.
Hull missed the opportunity to move seven points clear of the drop-zone but inched five clear and remain in 15th with Sunderland a place and a point behind, although QPR, Burnley and Leicester all have games in hand.
Blacks Cats manager Gus Poyet and Hull’s former Sunderland boss Steve Bruce had to be restrained and separated after a fiery touchline spat, which stemmed from Rodwell receiving a yellow card for simulation.