Chuba Akpom fired the visitors ahead 11 minutes into the second half before Charlie Colkett and Alex Kiwomya both scored in the space of seven minutes to turn the contest around.
The victory gives the young Blues a slender advantage ahead of the return leg at the Emirates next Thursday 17 April.
Afterwards, Blues coach Adi Viveash told the club's website: "It was a wonderful advert for youth football with two great sides going at it.
"It was a big physical exertion and we've just shaded it tonight but there's a long way to go and we know it's only half time in the tie. We've seen tonight what it's going to take to overcome this Arsenal team.
"I never doubted our ability to come back in the game. We did it at Newcastle in the last round and that's what happens when you get a positive result away from home coming from behind. Now that we've done it twice that will only build the belief in the group.
"We'll enjoy tonight but we'll wake up tomorrow and I'll start thinking about the second leg but a lot of the players will have to start thinking about Aston Villa away with the Under-21s on Monday. They're trying to win the league so there's a lot of games for us but come next Thursday we'll be ready for the challenge and we look forward to it."
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