There was little between the two sides at a sunny Brockhall, but the Gunners edged the match with a second half strike.
A competitive first half saw Rovers have a great chance in the 40th minute to take the lead when a long ball forward saw Modou Cham upended in the area by Arsenal goalkeeper Ryan Huddart.
But Huddart redeemed himself by saving Cham's spot-kick, diving to his right to make the stop.
The two young sides worked tirelessly but chances were at a premium, but it was the visitors who grabbed the only goal of the game 15 minutes from time.
A free-kick on the edge of the area was struck by Daniel Crowley, the ball taking a deflection off the wall and into the back of the net.
After that Rovers tried to get back in the game, playing with energy and thrust, but as had been the tale throughout, they couldn't create the opportunities to work the goalkeeper.
"Overall the only disappointment of the game was that we didn't create enough clearcut chances," said coach David Lowe.
"Our passing game and our energy was good but we didn't work their goalkeeper.
"It looks good for next season, it has given them a lot of experience playing a lot of youth team football and it should stand them in good stead."
ROVERS: Williams, Platt, Askew, Wharton, Nyambe, Hardcastle, Harris (sub Grayson 85 mins), Edgar (sub Mols 90 mins), Cham, Joel, Callaway (sub Haworth 77 mins).
Subs not used: Torres, Fisher.