Both teams enjoyed plenty of the ball during the opening stages, but the first real chance did not arrive until the 20th minute, with Franck Kessie firing over the crossbar after a Spurs mistake.
Milan almost gifted Spurs the lead in the 26th minute due to a mix-up in the defence, but Luke Amos watched on as the ball went agonisingly wide of the post after he had closed down the ball by the penalty spot.
Spurs made Milan pay for those misses by taking the lead within 80 seconds of the restart as N'Koudou ran towards the backline before unleashing a stunning effort into the top corner of the net from 16 yards out.
Hakan Calhanoglu tested the hands of Paulo Gazzaniga shortly afterwards before then curling a free kick narrowly off target, and the danger signs led to Mauricio Pochettino introducing both Christian Eriksen and Son Heung-min.
However, much of the closing stages passed by without incident and it allowed Spurs to end their tour of the United States with a hard-fought victory.
TOTTENHAM HOTSPUR (4-3-3) Vorm (Gazzaniga 46'); Walker-Peters, Sanchez (Carter-Vickers 92'), Eyoma, Georgiou (Davies 77'); Amos, Skip, Marsh (Aurier 77'); N'Koudou, Moura (Eriksen 63'), Llorente (Son 63')
AC MILAN (4-3-3) Reina (Donnarumma 46'); Abate (Antonelli 69'), Musacchio, Romagnoli, Calabria; Kessie, Locatelli, Calhanoglu (Mauri 78'); Suso (Halilovic 46'), Borini (Kalinic 70'), Cutrone (Tsadjout 78')
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