Josh Charnley gave the home side the lead after just four minutes, but Bradford soon claimed the lead, with efforts from Michael Platt, Adam Sidlow and John Bateman giving the visitors a 16-4 lead at the break.
The Warriors looked to reduce the lead at the start of the second half, but the Bradford defence was able to keep Wigan from scoring, while Jamie Foster was able to extend the Bulls' lead with a penalty.
Charnley got the Wigan comeback underway with less than 15 minutes to play, adding his second try of the game, with Tuson crossing the whitewash two minutes later.
An Ian Thornley try tied the scores in the 78th minute, before Tuson completed his brace in the final seconds of the game.
The result keeps Wigan at the top of the Super League table, ending a two-match losing streak.