Grant Leadbitter's penalty midway through the second-half looked enough to give Town the win against promotion chasers West Brom but Chris Brunt struck in added on time to level the scores.
The former Sunderland midfielder, wearing the skipper's armband from the start for the first time, powered in from the spot after Damien Delaney had been fouled in the box.
Blues had chances to have extended the lead late on with Tamas Priskin denied by Scott Carson and were made to pay when Brunt stabbed the ball in from close range after Simon Cox's shot had been blocked.
Town made four changes to the side that lost at Southampton at the weekend, with Pablo Counago, David Norris and David Wright returning to the starting line-up and Jon Stead back in the side after suspension.
Albion dominated possession in the early stages, Jerome Thomas cutting in and firing just over, Brunt doing likewise on the right flank.
Roman Bednar failed to convert at the far post from Graham Dorrans' corner, Stead hooked over in Town's first sight of goal but it took a save low down from Arran Lee-Barrett to keep the scores deadlocked on 15 minutes, the 'keeper denying Bednar after a superb pass from Brunt and Gareth McAuley clearing the loose ball before Albion could pounce.
Norris headed over after Delaney had flicked on, Brunt then warming Lee-Barrett's hands with a 25 yarder. The 'keeper was at the heart of the action moments later when he brought down Bednar just outside the box, the covering defenders saving the 'keeper from a possible red card, referee Stuart Attwell showing a yellow.
Counago and Stead linked up well to set up Norris who flashed a shot across goal, while at the other end McAuley was in the right place again to clear from Bednar following a scramble in the Blues' box.
Good link up play from Counago carved open an opening for Norris that brought a save low down from Scott Carson, McAuley thumping a header wide from the resultant corner.
Youssouf Mulumbu picked up a booking for a foul on Counago, Stead sending a left footer wide before Robert Koren came the closest to a goal in the first-half, his flick over Lee-Barrett headed off the line by McAuley.
Jaime Peters was denied by Carson after Counago released him on goal with the half closing with Leadbitter and Dorrans going into referee Attwell's book after a minor disagreement.
Lee-Barrett was quick off his line to smother the danger from Bednar, then watched anxiously as the Albion striker headed inches wide after his throw had been intercepted by Thomas.
Norris shot at Carson after Counago had set him up, Delaney superbly clearing from Bednar's cross four yards out. Carlos Edwards replaced Counago on 63 minutes and seconds later Town were ahead, Jonas Olsson penalised for a foul on Delaney and Leadbitter did the rest from the spot.
Albion immediately replaced Koren with Ishmael Miller, Pim Balkestein then on for Wright at left-back for Blues. Roberto Di Matteo made a second change for the last 15 minutes, Filipe Teixeira on for Thomas, Miller then shooting straight at Lee-Barrett as Albion camped inside Blues' box .
Stead made way for Tamas Priskin, the Hungary international operating up front on his own, with Albion completing the changes with Cox on for Mulumbu.
Edwards fired high and wide from Priskin's pass as Town looked for that crucial second goal, Balkestein then having the home fans on his feet with a storming run down the flank, his shot blocked by Gabriel Tamas on the edge of the box.
Priskin could have sealed it for Blues but was denied by Carson and in added on time, Brunt forced the ball in to deny Town the three points.
Town: Lee-Barrett, Rosenior, McAuley, Delaney, D.Wright (Balkestein 71), Peters, Leadbitter, Norris, Colback, Stead (Priskin 78), Counago (Edwards 63). Subs not used: McLoughlin, Martin, Garvan, John. Booked: Lee-Barrett, Leadbitter
West Brom: Carson, Jara, Olsson, Tamas, Cech, Brunt, Dorrans, Mulumbu (Cox 79), Koren (Miller 66), Thomas (Teixeira 75), Bednar. Subs not used: Kiely, Mattock, Zuiverloon, Martis. Booked: Mulumbu, Dorrans, Olsson
Att: 19,574
