In what was a largely uneventful 45 minutes of pre-season action, the Gunners created the first meaningful opening of the contest in the 15th minute when youngster Alex Iwobi forced a save from Izwan Mahbud, who moments later denied Alex Oxlade-Chamberlain.
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However, Mahbud could do little to prevent his side from falling behind 15 minutes later.
A sliding challenge stopped Jack Wilshere in his tracks, but the loose ball dropped for Akpom 12 yards from goal and the forward powered a low shot beyond the 25-year-old keeper.
As the interval approached, Arsene Wenger's men continued to dominate proceedings, but they were unable to create any clear-cut opportunities of note.
Victory for the North Londoners would see them advance through to the final of the competition, where they would face Everton following their 5-4 penalty shootout victory over Stoke City earlier today.