In wintery conditions it was a close contest between two young hardworking sides with the Gunners edging the match courtesy of a goal from close-range just after the half hour.
Under the stewardship of David Lowe, Rovers started brightly, Modou Cham seeing a shot from the edge of the area tipped round the post before a swirling Callum Harris shot had to be dealt with by Josh Vickers in the Arsenal goal.
Arsenal saw a ball scrambled away off the line by Ian Vicars, but it was Rovers who continued to carve out the better opportunities, striker Deniz Pero denied from close-range after Harris pulled the ball back.
As is often the case, that miss would prove costly as three minutes later the visitors grabbed the lead. Failure to deal with a cross from the left allowed Arsenal forward Tarum Dawkins to ghost into the area to poke home.
The Gunners ended the half strongly, with Rovers stopper David Raya called into making a couple of important saves to keep the score down to just the one at the break.
Straight from the restart Arsenal wasted a great chance to double their lead, Kaylen Hinds the offender, firing just past the post when clean through on goal.
Rovers countered with a chance of their own, Modou Cham with a superb cross to the back post but Dean Rittenberg just couldn't get a vital touch.
As the weather worsened play became scrappier with Arsenal content to hold their own, long-range efforts from Dean Rittenberg and substitute Jordan Preston testing Vickers.
The best Rovers chance came in the final moments but after good approach play Ian Vicars headed onto the roof of the net with a looping effort.
ROVERS: Raya, Vicars, Langford, Wassi (c), Scott, Doyle, Rittenberg (sub Wall 85 mins), Torres (sub Joel 75 mins), Pero (sub Preston 60 mins), Harris, Cham.