Richard Hinds responded by heading against the crossbar, before Clayton Donaldson equalised just after the half hour mark for a young Tigers line-up.
But Danny Ekoku restored Bradford's lead in the 45th minute, beating three men before scoring what turned out to be the winner.
City will look to show their bouncebackability when they go to Barnsley in a week's time.
City line-up: Duke; Wiseman, Byron, Hinds, Cattermole; Hotte (Allanson), Fry, Keane, Anderson; Benson, Donaldson.
Un-used subs: Matthews, Wilkinson, Briggs, McGarry.