Manager Phil Parkinson made a double substitution in the 52nd minute and the move paid dividends as Hines equalised seven minutes later, snatching a share of the spoils in the first Yorkshire derby between the two sides for 16 years.
The former West Ham winger took a pass from ex-York left-back James Meredith before beating three players in a 40-yard run and then smartly slotting the ball past 'keeper Michael Ingham to register his first goal for Bradford.
Fellow substitute Garry Thompson saw his right-footed shot rebound off the upright just two minutes later, while striker Nahki Wells missed a good chance as Bradford pressed for a second goal but neither side could produce a winner.
Ashley Chambers gave York the lead a minute before half-time with a superb shot from just inside the penalty area after Jon Challinor's angled effort from the right was blocked.
