Goals inside the first 11 minutes from Ronan Murray and Connor Wickham booked Town a place in the Fifth Round of the Youth Cup.
Blues went in front on 10 minutes at Barnet's Underhill when Murray blasted in from 15 yards and strike partner Wickham repeated the feat with a low drive 60 seconds later.
Wickham, who played the 90 minutes, could have added a third early in the second-half but dragged his shot wide from inside the box when he had more time than he realised and although Arsenal had more of the possession, they rarely troubled Mirko Ranieri in the Town goal.
The Italy U17 international did have to move smartly to make one save but the hard working Town players in front of him closed down many of the Gunners' attacks.
The victory, Town's second over the Youth Cup holders this season, sets up Blues for a Fifth Round game against Fulham at Portman Road with the tie likely to take place in the first week in February.
