An own goal from Rory McArdle levelled matters early in the second half after Jason Kennedy fired City ahead after just 44 seconds and further goals arrived from the excellent Sam Winnall and late sub Kane Hemmings.
Winnall was on hand to convert Lewin Nyatanga’s low cross in front of the Pontefract Road end from point-blank range on 65 minutes, just his third goal for the Reds since his six-figure move from Scunthorpe United in the summer.
It was just reward for the former Iron and Wolves frontman, golden boot winner in League Two with 23 goals last term, who turned in an impressive performance along with his team-mates, with the hosts dominating proceedings in the second period, a half crowned by a stoppage-time strike from Hemmings.
All this after City gave themselves a dream start with an opener inside the first minute when Jason Kennedy fired home low past Ross Turnbull, who failed to keep out the effort after good initial work from Mark Yeates.
Despite the blow, the Reds dusted themselves down and forged several decent first-half chances, but Jordan Pickford showed his mettle to make some telling saves.
The loanee clawed away a fine long-ranger from Luke Berry and beat away a stinging shot from Winnall, who also went close with a header which was grasped in the nick of time by the Bantams custodian.
Winnall also clipped the bar with a fierce strike with Hourihane also going close.
The Reds finally got their reward four minutes into the second half when McArdle, under pressure from Nyatanga, diverted Hourihane’s well-flighted free-kick past Pickford.
The hosts proceeded to dominate much of the second period and got a deserved winner when Winnall fired home following good work by Hourihane and then Nyatanga.
Winnall was then denied by Pickford, with chances at the other end at a premium in the second period as the home defence stayed resolute with Barnsley inflicting the first away league defeat upon Bradford this term.
Gloss was provided when Hemmings coolly stroked the ball home with virtually the last kick of the game after Hourihane’s shot was blocked.
Barnsley: Turnbull; Bree, Ramage, Cranie, Nyatanga; Cole (Lita 90), Hourihane, Bailey, Berry, R Williams (Brown 86); Winnall (Hemmings 90). Unused substitutes: Dudgeon, Treacy, Davies, M’Voto.
Bradford City: Pickford; Darby (Bennett 87), McArdle, Davies, Sheehan, Kennedy, Yeates, Liddle, Knott (Morais 62), Mclean, Clarke (McBurnie 79). Unused substitutes: B Williams, Meredith, Dolan, Routis, Bennett.