Goals in each half from Dean Rittenberg and Modou Cham saw Terry McPhillips' young side triumph at London Colney.
Rovers started the game brightly and should have taken the lead after just two minutes. Bradley Bauress with an inswinging free-kick from the right saw Cham head at the near post but the ball flashed wide of the upright.
Undeterred Rovers continued to force the pace and deservedly took the lead just past the midway point of the half.
Again it was Bauress in the thick of the action and as he centred from the left, the ball deflected in the area to where Dean Rittenberg was the quickest to react to stab the ball home from close range for his first goal of the season.
The start of the second half couldn't have gone better for Rovers as they doubled their lead just a minute after the turnaround.
Good tenacity in the centre of the park saw Rovers rob Arsenal of possession before Brice Wassi played Cham in one-on-one and he cooly slotted home.
Rovers then had to withstand a spell of pressure, but they defended resolutely, almost grabbing a third when a one-two saw Cham set Rittenberg away but his chip over the advancing goalkeeper flew inches over the bar.
"It was a really good team effort from our young lads," said coach Terry McPhillips after the game.
"We played some lovely stuff, scoring two good goals and we could have had more.
"There were some good individual performances and we can now look forward to Aston Villa next week."
ROVERS: Raya, Laverty (sub Scott 72 mins), Bauress, Torres (sub Jacobs 90 mins), Butterwick, Paul, Rittenberg, Wassi, Pero, Poole (sub Harris 76 mins), Cham.
Subs not used: Grant.