This time, Rovers looked to be coasting to a comfortable victory after taking the lead with just 45 seconds gone.
Bradford had other ideas, though, and despite playing well below their best they scrapped their way to an unlikely point - their fourth draw on the trot.
Rovers began like an express train, exposing the lack of pace in the home defence, and the opening goal came from a classic move.
Marc Rankine swapped passes with Ryan Taylor down the right flank, allowing the full back to drive to the line before hitting a low cross which was slammed home by Iain Hume.
Still shell-shocked, Bradford were struggling to contain the visitors as they launched a series of quick-fire raids.
The counter attack, when it came, would have brought an equaliser but for the lightening reflexes of Tranmere keeper John Achterberg.
He brilliantly palmed away Marc Bower's header from a Nicky Summerbee cross as the Bantams slowly began to put some moves together.
A minute later Lee Crooks tried his luck with a long range shot that flew wide of the target. As the interval neared, Rovers showed they were still dangerous, mounting an attack which ended with Paul Hall planting a header straight into the keepers arms.
The second half was punctuated by fouls and sloppy passing, with Bradford desperately seeking an equaliser and their guests clinging onto what they had.
It was only as the game entered its last 15 minutes that things really started to happen. In the 76th minute Summerbee whipped in a perfect curled cross which Dean Windass powered into the net with his head.
Tranmere, who by this time had already had three players booked, then had two more shown the yellow card and defender Gareth Roberts sent off in what would seem to have been a case of mistaken identity.