Rangers manager Jim Magilton was absent for the first time following his suspension pending an internal investigation.
Akos Buzsaky was not in the visitors’ matchday 18 due to injury, but temporary managers Steve Gallen and Marc Bircham looked to have enjoyed a debut to remember.
For all Albion’s dominance, they failed to punish the visitors and a Jonas Olsson own goal was quickly followed up on the hour mark by Kaspars Gorkss’ header.
But West Brom never gave up and Jerome Thomas reduced the deficit before Cox’s late, late leveller.
The result leaves Rangers without a win in eight games while second-placed Albion have stretched their advantage over the chasing pack to four points.