In a one-sided first half, Christian Benteke opened proceedings with a stunning strike from the edge of the area, before Gabriel Agbonlahor doubled the Villans’ lead before the interval by concerting a well-worked team goal.
The second half , however, produced a revitalised West Brom immediately pull one goal back through Brunt, before Odemwingie volleyed home the all-important equaliser eight minutes from time.
Steve Clarke made two changes from the 3-2 defeat against Reading, bringing in Claudio Yacob and Odemwingie for George Thorne and Jerome Thomas.
The away side, meanwhile, receive a boost as captain Ron Vlaar returned following a long lay-off, while Joe Bennett and Agbonlahor eplaced Brett Holman and Andreas Weimann from the 1-0 defeat to Southampton.
The away side started on the front foot, with West Brom seemingly suffering a hangover from their shock defeat to Reading last time out, and Benteke’s impressive work rate up topped reaped rewards after just 12 minutes.
The striker received a pass fairly innocuously from Charles N'Zogbia with his back to goal, dropped a shoulder, spun sharply and fired an unstoppable effort into the far corner.
With the Baggies looking increasingly listless, the away side began to dominate proceedings and, with half an hour gone, extended their lead with just their second clear-cut opportunity.
Kieran Westwood combined well with N'Zogbia to allow the latter to find Agbonlahor near the edge of the area. The forward needed just two touches as he brought the ball inside and past Foster with aplomb.
West Brom came out after the break with a previously absent desire and pulled a goal back with a delightful effort from Brunt after just four minutes. Odemwingie, following an excellent run from deep, allowed Romelu Lukaku to feed Brunt 15 yards from goal, who side-footed powerfully into the top left-hand corner.
As the Baggies endeavoured to find an equaliser, the away side proved dangerous on the counter-attack as, after the pace of Agbonlahor left Jonas Olsson trailing in his wake, Foster produced a good save to keep his side in with a shout.
West Brom responded by stepping up their game and, midway through the second half, a Gareth McAuley header from a Brunt corner required a goalline clearance from Ciaran Clark.
Just minutes later, Odemwingie almost managed what McAuley could not as, after a hopeful long ball forward, he rounded Foster but, running at pace, he was unable to keep his footing and fired over.
However, as the game entered the final 10 minutes, Odemwingie finally pulled his side level after a Brunt corner was turned into his path by Olsson, the striker finishing acrobatically from six yards out.
West Brom almost managed to salvage an unlikely win as the game entered injury time, but Lukaku could only fire wide to leave the spoils shared.