Jamaican winger Jermaine Johnson inspired Bradford to victory with a second-half winner against Cheltenham, who had John Finnigan sent off.
Kayode Odejayi gave Cheltenham the lead, before Jerry Gill cleared a David Graham effort off the line.
Finnigan was dismissed on the half-hour following an off the ball incident with City striker Dean Windass.
Bradford levelled on 52 minutes as Graham headed home and the winner came when Johnson ran clean through on goal.
Cheltenham: Brown, Gill (Elvins 73), Caines, Lowe, Armstrong, Melligan (Yao 84), Finnigan, McCann, Wilson, Odejayi, Guinan (Bird 34).
Subs Not Used: Puddy, Wylde.
Sent Off: Finnigan (32).
Booked: McCann, Bird, Gill.
Goals: Odejayi 4.
Bradford: Ricketts, Doyle, Wetherall, Bower, Edghill, Jermaine Johnson, Schumacher, Bridge-Wilkinson, Holmes, Windass, Graham (Colbeck 78).
Subs Not Used: Howarth, Parker, Eddie Johnson, Penford.
Booked: Windass, Bower.
Goals: Graham 52, Jermaine Johnson 69.
Ref: C Penton (Sussex).