Saido Berahino had struck his 18th goal of the season midway through the second half to cancel out Gabriel Agbonlahor’s 22nd-minute opener and put the visitors on course for a point.
But Villa claimed their first Premier League victory since 7 December – 12 matches ago – when Benteke kept his nerve and coolly side-footed home a spot-kick in second-half injury-time.
Sherwood had said in the build-up to the game that Villa would need to win six of their remaining 11 league fixtures to have any chance of avoiding relegation and after a slow start to proceedings where home nerves were evident, his team took control of the contest.
Agbonlahor thought he had given Villa a 14th-minute lead, but after producing a clever turn in the area and getting a shot away which Ben Foster somehow allowed to squirm under his body, the goalkeeper just managed to react in time to recover the situation before the whole of the ball had crossed the goal-line.
That near miss was soon forgotten when eight minutes later Agbonlahor did open the scoring after some route-one football, not that the Villa faithful cared about how the goal came about.
Villa ‘keeper Brad Guzan launched a back-pass high upfield before Benteke flicked the ball into the path of the onrushing Agbonlahor, who just beat the offside trap before keeping his nerve to shoot low past Foster at his near post.
That strike gave the Villa players a huge lift in confidence and they were unlucky not to double their advantage.
After another long clearance upfield Agbonlahor found himself one-on-one with Foster, only for Joleon Lescott to just get back in time to clear the frontman’s shot off the line for the second time in the opening period.
Then, in first-half injury time, Fabian Delph twisted and turned on the left-hand edge of the West Brom box, only to see his curling effort beat Foster’s outstretched hand, but not the post.
But Villa’s exertions in the opening 45 minutes soon began to catch up with them and, as Sherwood may have feared as those first-half chances went begging, West Brom found themselves on level terms with their first effort on target after 66 minutes.
The visitors played a left-wing corner high to the back post where Lescott lost Agbonlahor and his flick back across goal was headed in by the ever-alert Berahino for his 12th league goal of the campaign.
A tense Villa Park almost boiled over when Berahino and Alan Hutton squared up, the latter catching the frontman with a high boot that might well have earned him a red rather than yellow card.
Villa, though, were not to be denied as Sherwood urged his players forward in search of a winner, which came their way when Foster initially fumbled the ball and then, when trying to make up for his mistake, brought down Matthew Lowton.
Benteke, who had not scored since netting against Manchester United on 20 December, took the spot-kick responsibilities with aplomb to easily beat Foster and move Villa out of the drop zone in the process.
Charlie Nicholas’s verdict:
Villa were much better in the first half, they scored a fine goal, then when it went 1-1 you thought they were going to cave in. But Foster gave them a lifeline and Benteke, what coolness, he has been so out of form but he was covered in ice he was so cool.
Aston Villa: Guzan (6), Hutton (7), Okore (7), Clark (6), Lowton (7), Westwood (6), Cleverley (6), Delph (6), N’Zogbia (5), Benteke (6), Agbonlahor (8)
Subs: Weimannn (6), Grealish (7), Bacuna (6)
West Bromwich Albion: Foster (5), Dawson (6), McAuley (7), Lescott (6), Brunt (7), Fletcher (7), Yacob (6), Morrison (6), Berahino (7), Gardner (6), Ideye (6)
Subs: Baird (6)
Man of the match: Gabriel Agbonlahor