United were given a flying start when on-loan Notts County midfielder Joss Labadie drilled the ball home from 12 yards in the third minute.
The Gulls' joy was short-lived though as Rory McArdle met skipper Gary Jones' free-kick with a header four minutes later.
City went ahead in the 18th minute as home goalkeeper Michael Poke failed to clear well from Nahki Wells and Garry Thompson crashed in a thumping right-foot shot from the edge of the box. And Poke was replaced by substitute keeper Martin Rice two minutes later.
United central defender Brian Saah had an opportunity to level on the half hour mark but he drove over from 12 yards as the ball dropped to him from a scrambled free-kick clearance.
Bradford increased their lead with a textbook goal three minutes after the break, centre forward James Hanson heading in at the far post from Thompson's deep cross from the right wing.