Watson, who left Albion during the summer to join Wednesday on a free transfer, drove the ball home through a crowded goalmouth to deny Albion a seventh home win of the season.
Albion, who had battered Wednesday in the second half before taking a deserved lead through Kevin Phillips' 10th goal of the season in the 76th minute, were left seething by Watson's late heroics.
At the final whistle, Albion's fuming manager Tony Mowbray charged across the pitch to confront referee Nigel Miller.
Miller had originally signalled just three minutes of injury time, but kept playing beyond that mark after Albion left-back Paul Robinson needed treatment
When Bostjan Cesar was unable to fully clear a cross, Watson pounced on the loose ball to drill home his first goal of the season past Dean Kiely.
Amazingly, Wednesday could then have gone on to win the game as it needed a smart save from Kiely to deny Deon Burton.
It was rough on Albion who dominated the match only to be frustrated by Wednesday goalkeeper Lee Grant. But Watson's strike ensured that manager Brian Laws, whose side did the double over Albion last season, was given something to celebrate in his 50th game in charge.
Albion were frustrated by the linesman's flag, Grant and the woodwork as they failed to make the most of their possession in the first half.
After overcoming a rocky start when Marcus Tudgay had a shot blocked by Cesar and Richard Hinds headed narrowly over the bar, Albion took control through Ishmael Miller.
His 20th minute cross was turned into his own net by Wednesday's Frank Simek, but the strike was ruled out for offside.
Zoltan Gera, Filipe Teixeira and Miller all went close from distance before Tudgay wasted Wednesday's best chance of the half when he headed Burton O'Brien's 37th minute free-kick just wide.
It would have proved to be a costly miss just three minutes later but for Grant.
Phillips set up Miller on the edge of the area and his rising left-foot drive was goalbound before Grant pushed up a hand to tip the ball over the bar.
Wednesday had another major let-off 60 seconds after Grant's heroics when a corner from Jonathan Greening found its way to Phillips, whose snap-shot crashed to safety off the foot of the post.
Grant continued to frustrate Albion in the second period - pulling off another three top draw saves in the space of ten frantic minutes.
First he again beat away a Miller pile-driver in the 55th minute - this time deflecting the ball away with his legs.
Eight minutes later he denied Phillips at his near post and then produced the save of the game by throwing himself full-length to his left to tip away a goalbound header from Paul Robinson.
But there was nothing he could do when Phillips pounced with what looked like the winner before Watson's late, late show.