Bradford went in front after 14 minutes with a first goal for the club from Raffaele De Vita.
Kyel Reid found the Italian-born summer signing from Swindon with a left-wing cross and, after De Vita saw his first shot cleared off the goalline by Danny Batth, he hammered the rebound into the net to give Bradford the lead.
Wolves then shook the Bantams with two goals in four minutes.
Millwall loanee James Henry equalised after 28 minutes, taking advantage of a mix-up between Gary Jones and James Meredith, which left him with a clear shot at goal and he scored with a 20-yard shot that appeared to go under goalkeeper Jon McLaughlin's body.
The visitors went ahead four minutes later when Henry's left-wing corner was partially cleared by the Bradford defence and Henry returned the ball into the goalmouth where the alert Richard Stearman reacted smartly to head the ball into the net.
Bradford's leading goalscorer Nahki Wells, who has missed the last four matches through injury, came on as a half-time substitute and had two goalbound shots in a frantic finish, but the visitors survived everything the home side threw at them.