Villa were without a Premier League win since December 7, but moved three points clear of the Premier League's bottom three amid exuberant celebrations from new manager Tim Sherwood on the touchline.
Benteke kept his cool in the 93rd minute, moments after West Brom goalkeeper Ben Foster lost his bearings in tearing from his goal to bring down Matthew Lowton, handing Sherwood his first league win since taking charge.
Gabriel Agbonlahor ended a 14-match goal drought to open the scoring in the 22nd minute as Villa dominated the opening half.
Nerves set in after Saido Berahino's 66th-minute equaliser, but Villa gathered themselves to launch a decisive late rally and boost their survival prospects.
Charles N'Zogbia was preferred to Scott Sinclair in the only change to the Villa line-up.
Berahino and Brown Ideye overcame respective foot and knee injuries, giving West Brom head coach Tony Pulis the opportunity to name an unchanged XI.
The forward duo failed to make the most of a fifth-minute opening and then saw little to encourage them during the early stages as Villa pushed their visitors back.
Agbonlahor was almost gifted an opener when Benteke squared for him to shoot and Foster embarrassingly fumbled before grasping the ball on the line.
West Brom backed off too readily for Tom Cleverley to fire over in the 19th minute and they fell behind when Benteke won a flick on from goalkeeper Brad Guzan's clearance and Agbonlahor sped away from Joleon Lescott to slot between Foster's legs.
The Villa attacker's trademark pace and West Brom's surprising weakness against the long ball were on show again in the 28th minute, but Lescott got back to clear from the goalmouth after Agbonlahor poked beyond Foster.
Pulis was left with plenty to ponder at the interval, having gratefully watched Fabian Delph's fierce drive cannon back off the inside of the upright.
Lescott found himself in the referee's notebook for bringing down the rampaging Agbonlahor after 52 minutes, Ashley Westwood sending the resulting free-kick over.
West Brom had barely created a chance of note as the hour approached, but should have been level when Craig Dawson escaped the attentions of Jores Okore to head Chris Brunt's free-kick wastefully wide at the near post.
Substitute Jack Grealish sidefooted weakly at Foster and the England goalkeeper kept out a stinging drive from Delph before switching from hero to villain.
Foster raced out to clatter into Lowton, leaving Benteke to score the winner from the spot as he did in the same fixture last January.
