Button was shown the red card by referee Andy Haines after 25 minutes as he raced to the edge of the penalty area and brought down the Bantams' leading scorer Nahki Wells with a reckless challenge.
The hosts took advantage by going in front four minutes before the break through striker James Hanson.
Winger Kyel Reid played the ball down the left to James Meredith and the full-back cut the ball back into the middle where Hanson scored with a 12-yard shot.
Wells added the second on the hour mark following a long clearance from keeper Jon McLaughlin.
Defender Tony Craig tried to head back to Jack Bonham, on following Button's dismissal, but sent the ball over the head of the substitute keeper and the in-form Wells followed up to tap the ball into the empty net for his seventh goal of the season.
Garry Thompson scored the third four minutes later with a powerful header from Reid's left-wing cross and Hanson added his second and Bradford's fourth with a header at the far post from Reid's in-swinging corner.