After a scoreless first half, the Gunners took the lead in the 49th minute when Bayern left back Louis Poznanski steered the ball into his own net.
The German champions, however, were back on level terms in the 71st minute when Robert Lewandowski nodded home Serge Gnabry's cross.
10-man Bayern hit three past Furth to extend Bundesliga lead
Both teams had chances to take control late before Arsenal's Tyreece John-Jules won possession and provided a nice cross to Nketiah to score the winner with two minutes remaining.
The International Champions Cup features 12 teams playing friendly matches in venues in North America, Europe and Asia.
'I can't wait to have that experience' - Arteta, Nuno preview 'special' NLD
Parker's Picks: Wins for Chelsea, Arsenal in NLD; Brentford to hold Liverpool