Second-half goals from Gary MacKenzie, Billy Clarke and Tony McMahon sent the 2,410 visiting fans home happy as the Rovers faithful were left to reflect on yet another home defeat.
Doncaster shot out of the blocks and nearly took the lead inside 30 seconds, but Jonson Clarke-Harris’ effort from Harry Forrester’s cross flashed just wide.
Bradford created their first real chance in the 24th minute when Clarke met Filipe Morais’ cross, but he could not direct his header on target.
The best chance of the half came two minutes shy of the break when Curtis Main composed himself on the edge of the box before smashing a fierce shot against the angle of post and bar.
Bradford stunned Rovers nine minutes into the second half when a frantic goalmouth scramble ended with MacKenzie bundling the ball home.
Rovers were almost level three minutes later, but Ben Williams produced an excellent save to keep out Dean Furman’s effort.
Stephen Bywater saved well from Billy Knott as City searched for a second, which duly came with 63 minutes on the clock when James Hanson broke away and teed up Clarke who drove home from the edge of the box.
Substitute McMahon rubbed Rovers’ noses in it in added-on time as he rifled home the third in a Bradford break away.