The Bantams dominated a one-sided first half, but when the chances came their way they failed to punish Brian Little's battling outfit.
Veteran striker Steve Claridge saw his glancing head go wide of the mark after 44 minutes and in the final attack before the interval City full-back Lewis Emanuel shot weakly wide after a sweeping counter-attack.
City boss Colin Todd deployed his new 3-5-2 formation in a bid to follow-up last weekend's victory at Yeovil and the strategy looked to be paying dividends as they stifled Rovers and put a stranglehold on possession.
Bantams keeper Donovan Ricketts didn't have a save to make in the first period, but Tranmere came out in more positive fashion after the interval.
After 52 minutes former Bradford defender Simon Francis tested the home defence with a right-wing cross but Delroy Facey's header was comfortably saved by Ricketts.
Two minutes later Rovers' midfield finally broke through but after a neat exchange on the edge of the City box Bantams full-back Darren Holloway made a vital challenge to stop Stephen O'Leary in his tracks.
Francis was almost embarrassed after 65 minutes when his sloppy play gifted possession to Bradford's dangerman Danny Cadamarteri.
The City striker, who had worked hard all match, surged forward but his fierce drive was well-covered by Rovers keeper Dino Seremet.
With 20 minutes to go Claridge got half a sniff in the six-yard box, but before he could take aim centre-half Ian Goodison lunged in to make a crucial clearance.
Rovers, who will be happy to maintain their recent climb up the table, almost nicked it, but skipper Michael Jackson scooped a difficult half-volley over the bar from 10 yards.
Todd threw on teenage striker Joe Brown in a late bid to grab the winner but the youngster failed to make an impact.