Gary Bowyer's side opened the scoring midway through the first half, when good build-up saw Hugo Fernandez swicth the play to Osayamen Osawe, who ran at his full-back before unleasing a 15-yard drive that flew into the bottom corner.
Fernandez missed a clear cut chance to double Rovers' lead, whilst Osawe hit the bar and Raheem Hanley fired over, as the visitors dominated the first half.
The second goal eventually arrived 10 minutes after the restart. After good work from Anthony O'Connor and Raheem Hanley, Jordan Slew danced his way in and shot inside the post.
Rovers had further chances to pull clear, but with five minutes remaining, a free-kick was dealt with poorly and FC United caught Rovers out from the subsequent short corner.
Bowyer said: "Overall, I was very pleased with how we went about the game, after an underpar performamce against Curzon Ashton. The lads have now set a platform to build on at Halifax on Saturday."
ROVERS: Urwin (Dilo 46), Anderson (Beesley 46), O'Connor, O'Connell, Wylie (Daly 60), Evans (Haley 46), Hanley (Cotton 60), O'Sullivan (Maclaren 46), Fernandez (Lenihan 46), Osawe, Slew.