Rovers turned on the style at Priestfield to record only their third competitive victory at Gillingham.
John Marquis, Mallik Wilks and Danny Andrew were on the scoresheet for Rovers, with a late goal for the home side doing nothing to take the gloss off the performance.
Grant McCann made a number of changes, with captain Tommy Rowe coming back into the starting line-up along with Matty Blair and Alfie May.
The first exchanges were very open, with Rowe scuffing a shot inside the opening couple of minutes and May blasting a powerful effort over shortly afterwards.
The game kicked into life as it entered the second half of the opening period, with May and Rowe again having efforts halted.
Marquis fired Rovers ahead with almost half an hour on the clock. Increasing pressure from the visitors saw Herbie Kane and May cause some real problems before the ball rolled into the path of Ben Whiteman - his shot was deflected into the path of Marquis who made no mistake.
Whiteman and Andy Butler threatened to quickly double the advantage with efforts which were blocked from a corner shortly afterwards, while it also took two good blocks to deny Wilks.
The Gills threatened largely from counter-attacks and set-pieces, with Gabriel Zakuani heading wide from a Callum Reilly corner the closest they came to levelling before the break.
The home side made a change at the break, sending on the experienced forward Tom Eaves, but Rovers were the first to threaten after the restart when Marquis drilled an effort just wide of the near post.
Rovers doubled their lead 10 minutes into the second period when Wilks capitalised on confusion in the home defence, eventually being able to slot the ball into the empty net and celebrate in front of the travelling Rovers fans behind the goal.
And the game was effectively killed off on the hour mark when a Herbie Kane corner was only half cleared by the home side.
The ball fell for Andrew, who nudged the ball into space before smashing a shot which landed in the bottom left corner.
Rovers pushed for a fourth, with Andrew trying his luck with a free-kick which was gathered by Holy at the second attempt.
Rowe also clipped an header wide following a Kane corner, while Marquis also had a late effort blocked.
There was an opportunity for Grant to rotate his squad in the final stages, with Jermaine Anderson replacing Rowe and Rieves Boocock making his Rovers debut when he replaced May.
The home side did force home a late equaliser, with Reilly credited with it, but it was too little too late for the Gills.