Goals from John Marquis, Mallik Wilks, James Coppinger and Matty Blair helped Rovers secure a second consecutive win and emphatically end the unbeaten start of hosts Walsall.
The Saddlers had led through Morgan Ferrier but Rovers back superbly to end a run of seven straight defeats against bogey side Walsall.
Rovers had much the better of the early stages but suffered a blow on 17 minutes when the hosts took the lead.
Andy Butler failed to make a good connection with his headed clearance from a Josh Ginnelly cross, sending the ball across goal where Ferrier darted in to head home from three yards.
Walsall had the better of play after taking the lead and took control of the ball in the middle of the park.
But Rovers fought back well and began to threaten once more. Marquis had a shot blocked from close range from a Matty Blair knockdown.
Rovers were then gifted a way back into the game when Walsall full back Luke Leahy inexplicably handled in a challenge for the ball with Joe Wright. Marquis slammed the resulting penalty into the bottom corner.
In what became a very ill-tempered affair, Rovers took control of the game in the second half and were soon out of sight.
On 59 minutes they were ahead. Ben Whiteman slid through a superb pass for Wilks who shrugged off his marker and slammed past Walsall keeper Liam Roberts.
And seven minutes later they put daylight between themselves and Walsall.
Wilks carried the ball out of his own half and flicked a pass to Coppinger who clipped a superb shot over Roberts and in off the crossbar.
With the game petering out, there was still time for one more from Rovers in added time.
Subsitute Alfie May galloped down the pitch and cut a pass back across the area which ran all the way through to Blair, who took a touch and smashed into the near top corner.
Walsall: Roberts; Devlin, Fitzwater, Guthrie, Leahy; Morris (Ismail 72), Osbourne (Ronan 53), Dobson, Ginnelly (Gordon 80); Ferrier, Cook. Subs: Dunn, Kinsella, Johnson, Wilson.
Rovers: Marosi; Mason, Wright, Butler, Andrew; Blair, Whiteman, Kane (J Anderson 75); Wilks (Taylor 84), Marquis, Coppinger (May 74). Subs: Lawlor, T Anderson, Amos, Beestin.
Referee: Antony Coggins (Oxfordshire)
Attendance: 4,546 (496 away)