An 83rd-minute strike from Kieron Morris was enough to secure the points for the hosts, after Regan Hendry had seen his earlier effort cancelled out by Andy Cook.
The win lifted Rovers out of the bottom two, while the Bantams are down in 18th after another disappointing result.
Bradford looked the more dangerous early on with Jamie Walker hitting the post from the edge of the box while Alex Pattison and Walker again were denied by Rovers goalkeeper Luke McGee.
But it was the home side who took the lead after 24 minutes when Harry Lewis in the City goal let Hendry’s long-range effort slip through his hands.
Rovers took the game to their opponents after the break but it was former Rovers man Cook who rose unmarked in the 55th minute to bring the Bantams level with his fifth goal in three games before substitute Morris snatched it late on.
AFC Wimbledon secured a third consecutive win as Omar Bugiel’s first league goal for the club secured a 1-0 triumph at Harrogate Town.
The Lebanon striker ended a 13-game drought in the league with a stylish sixth-minute finish.
Bugiel latched on to a loose ball before charging 20 yards unopposed to the home goal and used the outside of his foot to sumptuously find goalkeeper Mark Oxley’s bottom-right corner.
The lively visitors then went close to doubling their advantage when Ali Al-Hamadi burst into the box, but Oxley saved well.
After the break, Wimbledon continued to dominate and although Harrogate brought on strikers Luke Armstrong and Josh March they never looked like scoring.