Bob Taylor's goal ensured a 1-1 draw with Rotherham and second spot for Albion, who were denied a win when Jordao's late effort was not given.
Millers keeper Mike Pollitt was put under a great deal of early pressure from the home side, but when Igor Balis had the chance to shoot after a good move down the right, he could only find the side-netting.
Darren Byfield then went close after 19 minutes when he was picked out in the box by Paul Hurst, but his diving header went wide of the target.
The Baggies took the lead on 33 minutes when Taylor received the ball on the left-hand side of the area from Derek McInnes before cutting back inside and firing home into the far corner of the net.
The visitors were back on level terms just five minutes into the second half though when Byfield poked home from six yards out after a goalmouth scramble caused by Alan Lee's cross.
Minutes later and Neil Clement's cross from the right found Taylor near the byline, but he could only hit the post from a tight angle, before Daniele Dichio tested Pollitt with a header under pressure.
Chris Sedgwick bullied his way through a chaotic Albion box following a corner on 68 minutes, but his second attempt on goal went wide via the post, while moments later Stewart Talbot somehow headed wide when standing on the goal-line from another testing corner.
The Baggies were then denied all three points 10 minutes from time when Jordao's spectacular overhead effort from close range was cleared by Rob Scott, despite the ball having appeared to have already crossed the line.
West Brom will feel aggrieved they are only a point clear of Wolves in third place, although it was a valuable away draw for Rotherham, who edged three points away from the drop zone.