Following a scoreless draw after 90 minutes, Manchester United scored all five of its penalty attempts to hold off the Serie A side in the International Champions Cup.
The Red Devils scored each of their penalties, with captain Darren Fletcher converting the decisive kick after Marco Andreolli rattled his effort off the crossbar.
United created the best opportunities during the 90 minutes, particularly in the first half when Wayne Rooney, Juan Mata and Danny Welbeck cut the Italians apart with a thrilling passing move, only for Mata's low cross to the cut out.
Both sides made wholesale changes at the break, including Luke Shaw, who manager Louis van Gaal branded unfit 24 hours previously, and Wilfried Zaha, who played as a striker in his first appearance this pre-season.
Nani went close for the Premier League side, cutting in from the right and exchanging passes with fellow substitute Shinji Kagawa, but his right-footed strike went over the bar. Shortly afterwards he forced Juan Pablo Carrizo into a routine save with a low shot after he was picked out by Fletcher.
In between those two efforts Cleverley almost broke the deadlock himself, but his volley from just inside the area flew over the crossbar.
Van Gaal's men then thought they should have had a penalty when Tom Cleverley was brought down in the area, but the referee was unmoved despite what was a clear trip.
With neither side able to find the breakthrough the match went to penalties, and with Ashley Young, Javier Hernandez, Tom Cleverley, Shinji Kagawa and Fletcher all on target the Red Devils picked up two points for the victory, with Inter taking one.