League Two leaders Brentford looked set for victory as the match went into stoppage-time until Thorne struck with his 15th goal of the season.
Northern Ireland international winger Steve Jones played the ball into Thorne and, although his first shot was blocked by keeper Ben Hamer, the veteran striker managed to squeeze the rebound into the net.
Brentford controlled large sections of the match and deservedly went in front in the 63rd minute through Billy Clarke.
The on-loan striker reacted quickest to Ryan Dickson’s cross and slotted home a near-post header to open the scoring.
Karleigh Osbourne and Damian Spencer both went close as Brentford dominated the first half hour, but Chris Brandon missed a great chance to put Bradford in front two minutes before half-time when he was left with only Hamer to beat but he could find no way past the Bees stopper.