The game was twice held up by floodlight problems, but Gary Owers' side ran out comfortable winners.
Julian Alsop converted Alex Meechan's pass just seven minutes in to break the deadlock and Paul Wanless quickly added a second by converting Jon Richardson's free-kick to take his tally this season to eight.
Tim Sills gave the Shots hope right on the stroke of half-time, but Guy Madjo restored the two-goal cushion just three minutes after the restart.
The on-loan Bristol City striker added his second 19 minutes from time, heading home an Alsop cross from close range.
Madjo should have completed a hat-trick as full-time approached, but placed his penalty over the crossbar after he had been brought down by Gary Holloway.
Hassan Sulaiman gave the visitors a late boost with an injury-time strike, but Rovers had done more than enough to make it seven points out of nine in their last three league games.
For the Shots the result continued a dreadful festive campaign to date, with Terry Brown's side having been thrashed 4-0 at Exeter on Boxing Day.