United converted all of their kicks in the shoot-out at FedEx Field, Darren Fletcher slamming home the winner after Marco Andreolli had hit the crossbar.
Having beaten Roma last week, United have one foot in the final of the International Champions Cup, where they could face Manchester City.
United's new signing Luke Shaw, who van Gaal had described as unfit on the eve of the game, came on to play wing-back for the second half, while Wilfried Zaha, who showed plenty of promise on his first appearance of the tour, was introduced to play up front.
Former United stalwart Nemanja Vidic was in the Inter line-up and made a key challenge on Zaha before he was substituted with 18 minutes left.
Van Gaal’s men were sporting their new blue kit for the first time but, although they passed the ball around nicely before the break, they struggled to create clear-cut chances.
Phil Jones went closest, drawing a good save from Samir Handanovic with a header from a corner, while Juan Mata and Wayne Rooney were off target with shots from distance.
The Manchester United boss made eight changes at the break and his team began to look more dangerous.
Tom Cleverley volleyed over the bar and Juan Pablo Carrizo then denied Nani from close range, before Shinji Kagawa was thwarted by Danilo D'Ambrosio when he tried to turn in the rebound.
United then had a pair of penalty shouts turned down by ref Edvin Juisevuic in quick succession, as Zaha and Cleverley went down in the box.
Inter were kept fairly quiet throughout but David de Gea had to make a good late save from a Fredy Guarin free-kick.
And Zaha almost won it for United in the final minute, shooting into the side netting after a mazy run into the box.
That meant penalties and both sides converted their spot-kicks with aplomb until Andreolli's miss, Fletcher, Ashley Young, Javier Hernandez, Cleverley and Kagawa on target for United.