Harlequins ended the world champions' run of 14 victories, but really deserved to come away from Odsal with both points after a gutsy performance from a weakened side.
Paul Deacon missed two relatively easy goal-kicks for Bradford as they tried to wear down their stubborn opponents in the second half, but his long- range penalty three minutes from time salvaged a draw.
With Luke Dorn and Tyrone Smith missing as well as Mark McLinden, the Londoners' line-up looked below par from the outset in their first away game under their new title.
They began to look even more stretched when Matt Gafa was sent to the sin-bin after five minutes. He had covered back in defence to deny Michael Withers a length-of-the-field try, but then hung on too long in the tackle. No sooner had he departed than the Bulls scored their first try, from Paul Johnson's pass to Ian Henderson. It looked ominous for Harlequins, but the New Zealand scrum-half, Thomas Leuluai wriggled and twisted his way over for a quick reply.
Quins could even have gone ahead soon after their team was restored to its full complement, but Leuluai knocked on from Gafa's break. By this time, Quins had a 19-year-old from Gravesend, Tony Clubb, making his debut in the centres, but the Bulls' attempts to exploit any uncertainty on his part came to nothing, amid a welter of attacks that broke down through bad handling. Worse than that, they were alarmingly fallible in their own territory and were punished when Withers lost possession on the half-hour.
Rob Purdham was stopped on the line for Harlequins, but Leuluai's pass sent the substitute, Danny Williams, through and Paul Sykes' second goal gave the visitors a shock six-point lead which they had little difficulty in holding until half-time.
Iestyn Harris started to put matters right two minutes into the second half with his run and pass to set up Shontayne Hape, although Deacon's simple conversion attempt hit the post to leave Harlequins in the lead.
Within another couple of minutes, Bradford were ahead, Stanley Gene kicking through, Rikki Sheriffe fumbling and Ben Harris capitalising. That did not flatter Quins, especially Leuluai, who combined with Gafa just after the hour to send Lee Hopkins over for a converted try.
Deacon missed another goal he would normally expect to kick when Bradford were awarded a penalty seven minutes from the end. Much of the remaining time was spent battering the Harlequins' line before Deacon finally got one on target after Williams was caught offside. Even then, Sykes' drop-goal attempt in the last minute could have won it for Quins and that would have been no injustice.
Bradford: Withers; Bai, B Harris, Hape, Pryce; I Harris, Deacon; Fielden, Henderson, Lynch, Johnson, Meyers, Langley. Substitutes used: Vagana, McKenna, Gene, Cook.
Harlequins: Luisi; Sheriffe, Sykes, Purdham, Bradley-Qalilawa; Gafa, Leuluai; Temata, Weisner, Heckenberg, Haumono, Hopkins, Mbu. Substitutes used: Williams, Clubb, Mills, Tookey.
Referee: A Klein (London).