Former Great Britain winger Gareth Raynor was sent off after half-an-hour for a foul on Sam Tomkins (pictured) as the England full-back was going over for a try that put the Super League champions into the lead for the first time.
The Bulls winger appeared to be aiming to dislodge the ball from Tomkins' grasp but referee Steve Ganson decided there was intent to harm the player, although he opted not to award an additional penalty. Tomkins was out cold for several minutes and, after being helped to his feet, was taken from the field and played no further part in the eventful match.
The numbers were briefly evened up when Wigan prop Jeff Lima, no stranger to disciplinary matters in his first season in England, was sin-binned four minutes before half-time for use of the elbow.
But the champions seized control of the tie even before they were restored to their full complement, with the aid of two tries in the first five minutes of the second half.
Stand-off Brett Finch sprinted 70 metres for the first after collecting Kyle Briggs' kick and Pat Richards, switched to full-back in the absence of Tomkins, supported a break by winger Darrell Goulding to touch down for his second try.
At 22-6, 12-man Bradford were staring at a crushing defeat but they rallied superbly to belie the struggles that have undermined their Super League campaign.
Scrum-half Ben Jeffries, now in his second spell with the Yorkshire club, carved out a try for winger Patrick Ah Van and full-back Shad Royston pounced on Briggs' grubber kick as the Bulls cut the deficit to just four points.
Wigan finally made the game safe with second-rower Liam Farrell's 75th-minute try but the Bulls scored the game's last try through Ah Van.
St Helens eased into the Challenge Cup quarter-finals with a comprehensive 70-0 victory over Featherstone.
The Championship title-chasers did not disgrace themselves, especially in the first half, with the final scoreline not doing their effort justice.
Saints, without 11 injured first-team players, scored 12 tries in the game, with Michael Shenton and Thomas Makinson both scoring a brace.
Influential scrum-half Danny Brough created three tries and kicked three goals to help Huddersfield Giants through to the Challenge Cup quarter-finals thanks to a 30-16 win over Catalan Dragons.
Jermaine McGillvary, Leroy Cudjoe, David Hodgson, Kevin Brown (two) and Darrell Griffin were the try-scorers for the Giants, who were just two points ahead at the break.
Ian Henderson, Jean Philippe Baile and Jamal Fakir touched down for the Dragons, with Scott Dureau kicking the rest of their points.