The 35-year-old's injury-time finish was his most important of the season so far after League Two leaders Brentford looked to be heading for a ninth victory on their travels this season.
Bees keeper Ben Hamer was hardly tested as the visitors dominated the second half and the three points looked to be in the bag after lively striker Billy Clarke headed them in front after 62 minutes.
But with City desperate to take something from the game they staged a late rally and got their reward when Thorne poached the equaliser in the dying minutes.
The Bantams' leading scorer reacted smartly to Steve Jones' low cross and when Hamer could only push the ball away, Thorne got to his feet to drill in the leveller from four yards out.
The Bees, who remain on course for automatic promotion, will feel like they let two points slip but a draw was probably a fair result after an even first period.
The visitors could have gone ahead after just eight minutes when full-back Karleigh Osborne saw his volley from a deflected free-kick hit City keeper Rhys Evans and bounce away.
Striker Damian Spencer then failed to connect properly with a close-range header with the City goal at his mercy.
But Bradford gradually got back into the game and Thorne came close to putting them ahead when he ran on to Paul Mullin's excellent cross only for Hamer to snuff out the danger with a brave block.
Just before the break Mullin and Thorne combined again in City's best move, but midfielder Chris Brandon wasted the chance when his shot was again well saved by Hamer.
Bees' striker Clarke had proved a handful all game and he put the visitors ahead in neat fashion just after the hour mark.
Full-back Ryan Dickson overlapped on the left after a strong run by Sam Wood and when the cross came over Clarke darted between City's defenders to head in the opener from eight yards out.
The leaders seemed to have a grip on the game for the remainder of the match, but City's late surge unsettled them and Bradford did just enough to grab a share of the spoils thanks to Thorne's last-gasp equaliser.