Hull KR scrum-half Michael Dobson landed a last-minute drop goal to deny Bradford victory in a thrilling finish at Odsal.
Bulls captain Paul Deacon claimed a drop goal of his own with two minutes remaining to edge his side 13-12 ahead but Dobson had the final stay in the dying embers of the game.
Rovers were on course for a hard-earned victory at half-time after establishing a 12-10 interval advantage through two tries from Peter Fox and two goals from Dobson.
They were forced to defend doggedly for the majority of the game but the Bulls, who also touched down twice in the first half through Semi Tadulala and Chris Nero, dominated the second period.
Deacon levelled the scores with 10 minutes remaining and then seized centre stage again with his drop goal before Dobson struck from distance to ensure the honours were shared.
Rovers stunned Bradford by opening the scoring inside the second minute when a 20-metre restart allowed Scott Murrell to begin a move which saw Fox embark on a run from deep inside his own half.
Fox showed blistering pace to leave a trail of Bradford defenders in his wake, voiding Michael Platt's weak attempts at a cover tackle and touching down etween the posts.
Dobson added the easiest of conversions to put Rovers 6-0 ahead and in the eighth minute that advantage was extended by another two points.
Sam Burgess, making his first appearance since last July after a shoulder injury which ruled him out of the World Cup last autumn, was punished for interference by referee Ben Thaler and Dobson added the resultant penalty.
Bradford, who handed debuts to Rikki Sheriffe, Nick Scruton and Steve Menzies, responded impressively and enjoyed long spells of sustained pressure.
However, too many passes were misplaced, undercooked or simply forward as the visitors defended their line with admirable doggedness.
Rovers stand-off Paul Cooke was placed on report for catching Ben Jeffries late and the Bulls, with Deacon a growing influence, began to build up a head of steam.
They were rewarded in the 27th minute when Glenn Morrison's neat short offload sent Tadulala over in the left corner.
Deacon converted the score with a fine touchline conversion but Bradford were stunned four minutes later when Rovers and Fox claimed a second try.
The visitors stretched their opponents out wide and Ben Galea's long pass allowed Fox to squeeze over in the left corner.
Dobson could not convert and five minutes before the break Bradford were dealt a blow when replacement David Solomona was forced off after sustaining an arm injury and replaced with Matt Cook.
Yet the pendulum swung back in the Bulls' favour shortly before half-time when Terry Newton fed Morrison and he produced another telling pass to usher Chris Nero over in the left corner.
Deacon could not add the conversion that would have levelled the scores and while Bradford continued to probe after the restart, they created precious little.
And they were dealt a blow shortly before the hour mark when Jamie Langley succumbed to a shoulder injury.
Rovers' defending was outstanding in the second period as Bradford increased the pressure, but Paul Sykes could not take Burgess' delicate offload in his stride with the try-line begging.
However, salvation arrived for Bradford with 10 minutes remaining when Deacon slotted home a penalty from under the posts.
Deacon then added a drop goal in the 78th minute before Dobson did likewise with the last play of the game.