A US record crowd of 109,318 watched United's new manager rack up his fourth win of the summer thanks to two goals from Ashley Young and another from substitute Javier Hernandez. Even the second-half introduction of former United star Cristiano Ronaldo could not help an out of sorts Madrid, whose only goal came courtesy of Gareth Bale's penalty.
Van Gaal, who has recorded wins over the Los Angles Galaxy, Roma and Inter Milan in the US, will now take his squad to Florida for the final of the International Champions Cup. There, Van Gaal will get his first taste of United's bitter rivalry with Liverpool, who qualified for the final after Manchester City lost 5-4 on penalties to Olympiacos following a 2-2 draw in Minneapolis.
Real Madrid's starting XI did not include Ronaldo, and new signings Toni Kroos and James Rodriguez, but there were still plenty of stars on show in white. The likes of Bale, Luka Modric and Xabi Alonso were second best in the opening half though as United dominated from the off.
Darren Fletcher in particular impressed early on. The Scot dictated play from deep, spraying passes across the vast surface in Ann Arbor. United's captain for the night flashed a shot wide from 20 yards after 13 minutes and soon after he played a crucial part in the first goal.
The midfielder played the ball into Wayne Rooney, who returned it with a deft backheel. Fletcher then squared to Danny Welbeck, who teed up Young and he drilled the ball past Iker Casillas at his near post.
It took Carlo Ancelotti's team just six minutes to equalise though. Michael Keane, making his first start of the tour, clambered all over Bale's back and the Welshman went to ground to earn a penalty. The former Tottenham winger converted the spot-kick to David de Gea's left.
Bale tested De Gea with an overhead kick, but United remained on top and they deservedly regained the lead nine minutes from half-time. Young cut in from the left and floated a ball to the back post. Rooney missed as he jumped for the header, but his body movement was enough to wrong-foot Casillas and the ball sailed in at the far post.
Welbeck suffered an injury and came off for Wilfried Zaha just before the break. Van Gaal made three substitutions at half-time, and another three on the hour.
Bale struck the post with a dipping free-kick. Madrid fans called for Ronaldo's introduction, yelling his name as he warmed up on the touchline. Then, with 17 minutes left, the decibel levels rocketed inside the Michigan Stadium as Ronaldo replaced Alvaro Arbeloa. The Portuguese wowed the crowds with a couple of neat step-overs, but he could not swing the match in Real's favour.
Hernandez put the result beyond any doubt when he nodded in Shinji Kagawa's pin-point pass from close range in the 80th minute.