Charlie Austin's late penalty secured a dramatic 2-1 victory as Albion saw off Sheffield Wednesday in front of a sell-out Hawthorns.
Austin, who headed against a post just moments earlier, slammed home his third goal of the season in the 88th minute to seal all three Sky Bet Championship points after Keiren Westwood had blocked Matheus Pereira in the penalty area.
Hal Robson-Kanu had earlier converted his fourth goal in six games to put the Baggies in front, only for Steven Fletcher to level matters with a 58th-minute penalty.
It was an end-to-end encounter in front of 25,566, with Barry Bannan and Morgan Fox also hitting the woodwork for the Owls, who saw Liam Palmer sent off late on for a dangerous challenge on Grady Diangana.
Austin's late spot-kick secured a third successive victory and ensures Slaven Bilić's table-topping side are now unbeaten in seven matches, with Bristol City the visitors on Wednesday.
The Baggies head coach recalled Filip Krovinović and fit-again Ahmed Hegazi, making his first appearance of the season, to replace suspended pair Jake Livermore and Romaine Sawyers.
And, amid an open start to proceedings, there were early chances at both ends, Owls skipper Bannan seeing his inswinging corner rebound off the near post.
Yet it was Albion who struck first with just 10 minutes on the clock. Pereira picked up the ball in the middle of the park and played a superb throughball for Robson-Kanu to convert past Westwood.
The encounter continued to be played at a high tempo, with the hosts dominating possession, although neither side could create a clear-cut opening and the Baggies held a slender lead at the interval.
Yet it was all square just before the hour mark as the resurgent visitors levelled matters courtesy of Fletcher's spot-kick, awarded after Krovinović was adjudged to have upended Kieran Lee.
Robson-Kanu came within inches of an immediate response at the other end before Fox clipped the crossbar for the Owls as the clash continued to flow from end to end.
Robson-Kanu narrowly failed to connect with Matt Phillips' low cross in the 69th minute
Bilić turned to substitutes Austin, Chris Brunt and Gareth Barry, his first outing since March after a knee injury, in a bid to find a breakthrough.
And it came just two minutes from time.
Austin, having already seen a header rebound off the woodwork, stepped up to convert from the spot after Westwood's foul and spark celebratory scenes among the home faithful.
The visitors' misery was compounded in the 92nd minute when Palmer was given his marching orders, with Albion unbeaten in seven league meetings against the Owls stretching back to 2007.
Albion: Johnstone, Furlong, Bartley (c), Hegazi (Barry 74), Townsend, Krovinović (Brunt 80), Ajayi, Phillips, Pereira, Diangana, Robson-Kanu (Austin 75).
Subs: Bond, Gibbs, Edwards, Zohore.