Rovers' victory brought the hosts' eight-match unbeaten run to an end.
In a game of few clear chances Lowe broke the deadlock in the 69th minute, beating keeper Jon McLaughlin with a low, angled shot into the far corner after Jake Kirby had flicked the ball into his path.
Tranmere were grateful to keeper Owain Fon Williams for a brilliant diving save to keep out substitute Caleb Folan's header two minutes from the end.
A largely uneventful first half was marred by a melee in the 27th minute involving both sets of players and both benches after Tranmere skipper Ian Goodison appeared to elbow winger Kyel Reid in front of the dug-out.
Lincolnshire referee Darren Drysdale booked Goodison after consulting with the fourth official much to the anger of Bradford manager Phil Parkinson, who clearly thought the defender ought to have been sent off.