It was no more than the visitors deserved as they bounced back in style from falling behind to Jonathan Greening's strike to equalise through David Connolly.
As Albion chased a winner, Bullard struck to send Wigan's army of fans into ecstasy.
Albion failed to heed the pre-match warning of manager Bryan Robson who had told his side they needed to start putting the lower ranked sides in the Premiership to the sword.
But they lacked the cutting edge to see off Wigan, who have now Leapfrogged over Albion after their dramatic success.
Before Greening struck to break the deadlock, Wigan had been indebted to goalkeeper Mike Pollitt for ensuring they remained on level terms.
The former Rotherham goalkeeper pulled off a smart save to deny Darren Carter in the 11th minute, but was powerless to prevent Greening powering Albion ahead in 15 minutes later.
The goal was a defensive nightmare for Wigan who failed to deal with Steve Watson's cross, allowing Greening fire the loose ball at goal.
Pollitt attempted to punch the ball clear under pressure from Carter but only managed to send it back to the feet of Greening, who took full advantage of his second chance and drilled in a shot that took a slight deflection on its way into the back of the net.
It should have been the signal for Albion to take a stranglehold on affairs but they were unable to build on their advantage and allowed Wigan back into the game five minutes before half-time.
Connolly's equaliser was a high-class strike right from the flick-on by Damien Francis to the finish by the former Republic of Ireland striker.
Francis's flick set Connolly clear, but he was tracked every step of the way by Albion central defender Thomas Gaardsoe, who looked to have forced him too wide to get in a shot.
But the well-travelled marksman was able to wrap his left-foot around the ball and send his shot flying past goalkeeper Chris Kirkland.
Gaardsoe should quickly have made amends but he wasted a golden chance to regain the lead when he headed wide from just six yards.
Albion's frustrations continued into the second half when Nathan Ellington, who made a subdued full debut against his former club, saw his rising drive tipped over the bar by Pollitt.
Ellington was hauled off after 71 minutes as Robson gambled on a three-man attack of Geoff Horsfield, Robert Earnshaw and Kevin Campbell. But the trio could not find a way past Wigan's experienced central defensive duo of Stephan Henchoz and Arjan De Zeeuw.
As Albion chased the game it become inevitable that gaps would appear in defence and Wigan exploited that to the full in injury-time.
Former Baggies striker Jason Roberts, who was pilloried all afternoon by his former fans, rolled the ball across the face of goal into the path of Bullard, who beat Kirkland with a perfectly placed shot from the edge of the area.
Man of the Match: Jimmy Bullard
The hard working midfielder must have covered every blade of grass at The Hawthorns as he epitomised the kind of spirit that Wigan will need to win their Premiership survival battle.