Chris Brunt's scrambled last minute equaliser saw Albion move a point closer to the automatic promotion places.
The Baggies fought until the end after Jay Rodriguez's second half dismissal. Here's our player ratings:
Sam Johnstone: Couldn't do much with Albion's first but made a smart save from a similar position in the first half. Hardly touch the ball after the break. 6/10
Tosin Adarabioyo: Another error led to a goal conceeded for the Albion. Becoming Albion's weakest link - although he battles on despite being played out of position. 5/10
Craig Dawson: Did well to win the physical battle against Wednesday's giant centre forward. Worked the ball well and even unded up on right as Albion pushed forward for an equaliser. 7/10
Kyle Bartley: Looked shakey at times and clearly low on confidence. Didn't do too much wrong though against the Owls and won his share of aerial battles. 6/10
Kieran Gibbs: Didn't have the same impact first half when paired with Sako down Albion's left. Came to life after the break when partnered with Barnes and was another who pushed Albion forward for an equaliser. 7/10
Chris Brunt: Struggled to get a grip of the game in the first half but came into the game when Albion went down to 10. Then scored his first of the season with a swing of his left boot deep into injury time. 6/10
Jake Livermore: Was willing to take the initiative after Albion had gone one down but couldn't find a way through Wednesday's well drilled midfield. 6/10
James Morrison: Was a little unlucky to be subbed in the second half. Looked to be Albion's only bright spark in the first half and create a couple of chances with his keen eye. 6/10
Bakary Sako: Started down the left but then switched to the right. Looked threatening with the ball at his feet but looked really short of match fitness. Was no surprise when he was subbed. 6/10
Jay Rodriguez: Looked to have put the game out of Albion's reach with his dismissal. Albion will appeal but they could be without the hard working forward for a few weeks. 5/10
Harvey Barnes: Wasn't as effective out wide right before the break. But came to life after the break when he was reunited with Gibbs down the left. Looked threatening but couldn't find a moment of magic. 6/10
SUBS
Gareth Barry: Brought an assurance to Albion's midfield and kept probing for a way through Wednesday's back line. 6/10
Hal Robson-Kanu: Looked to have equalised with a fine looping header but was denied for a great save. Struggled to hold on to the ball at times but was willing to put in the hard yards to earn Albion a point. 6/10
Matt Phillips: Came on to play right back and was excellent going both ways. Gave the Baggies a direct threat down the right and his pin-point corner saw Albion equalise. A good cameo appearance. 7/10