All five United penalty takers found the net in a 5-3 showdown that followed a 0-0 draw after 90 minutes.
United only registered one shot on target in the first half, but they upped their game after the break.
Substitute Wilfried Zaha, making his first appearance of the tour, was particularly impressive playing as a striker, as was Luke Shaw.
Zaha, and Tom Cleverley were unlucky not to be awarded penalties in normal time at the FedEx Field.
David de Gea only had one save to make during the match and he watched Marco Andreoli hit the bar from 12 yards, which allowed Darren Fletcher to fire home the winner.
Fletcher, Ashley Young, Javier Hernandez, Cleverley and Shinji Kagawa all scored fine penalties.
It was a far better performance from 12 yards than the dismal 2-1 shootout defeat to Sunderland under David Moyes last year.
After beating Roma last week, United now have one foot in the final of the International Champions Cup, where they could face Manchester City.
It was an exciting end to a match that offered very little at the start.
The only flash point of the first half came when Phil Jones got in front of his marker to meet Juan Mata's corner, and Samir Handanovic saved acrobatically before smothering the ball.
Wayne Rooney cleared the bar and Juan Mata also belted a 25-yard shot just wide, but otherwise Handanovic had nothing to do.
United were passing the ball well, but they lacked energy in the final third.
Van Gaal looked to inject life into the match by bringing on eight players at half-time.
The likes of Rooney, Ander Herrera and Mata came off and Kagawa, Nani and Cleverley came on.
Shaw, who Van Gaal declared was unfit on the eve of the game, was given a chance to prove himself.
Another second-half substitute with something to prove, Zaha, made an early impact, racing through the Inter defence before former United centre-back Nemanja Vidic came to the rescue with a last-gasp intervention.
It proved to be the Serb's last significant act as he was substituted with 18 minutes to go.
Cleverley volleyed a shot just over the bar as United upped their game in the final quarter of the match.
Juan Pablo Carrizo parried Nani's effort from the close range and the ball fell to Kagawa, but he was blocked by Danilo D'Ambrosio.
Zaha's tidy step-over took him into the box, but he was brushed off the ball
The former Crystal Palace man appealed for a penalty yet Edvin Juisevic waved play on.
The referee denied United another penalty moments later when Andreoli swept Cleverley's legs from underneath him.
Van Gaal brought on Hernandez for Nani, who had only been introduced at half-time.
Van Gaal strode the touchline and shouted towards the referee when he gave a foul against Cleverley when he won the ball.
De Gea was called into action for the first time when he saved well from Fredy Guarin's free-kick.
Zaha almost snatched a winner for United in normal time after a mazy run into the box.
When penalties came, United's takers were all fearless
Inter's were too, until Andreoli stepped up and hammered the ball against the bar.
Source : PA
Source: PA