A stunning individual performance from Memphis inspired United to a commanding- if not quite yet unassailable- lead in the Champions League playoffs over the ten man Belgians.
The 21-year-old, signed from PSV for £25 million- scored twice and set up the nerve-settling third for Marouane Fellaini to put the Reds in command and give them one foot in the group stages.
The early stages did not go to plan for Van Gaal's side, though, as Brugge started well and stunned Old Trafford when they took an eighth minute lead through Michael Carrick's unfortunate own goal from a Victor Vazquez free-kick.
The equaliser was not long in coming, though, and it took the hosts only five minutes to restore parity after Memphis juggled the ball, cut inside and rifled home an excellent low drive.
Depay had an effort well saved by Brugge keeper Sebastien Bruzzesse and Wayne Rooney- again on the fringes of the game- had an acrobatic scissor kick cleared off the line as United started to come on strong.
The hosts ramped up the pressure and reaped the rewards shortly before the interval through another brilliant strike from Memphis who curled home a wonderful 25-yarder after good work from Daley Blind.
Juan Mata and Memphis went close to a third as the visitors- backed noisily throughout by their travelling fans- began to tire.
At 2-1, the hosts could not afford to ease off and should have extended the lead just before the hour mark as Memphis missed a golden opportunity for his hat-trick.
The winger blazed over from ten yards when well-placed after a neat flick from Rooney when it looked easier to score.
In truth, the Reds never really looked like relinquishing their lead, and, after Mata went close with a drive and Adnan Januzaj also flashed a shot wide, Brugge were reduced to ten men when Brandon Mechele was sent off for a late tackle on substitute Chicharito to earn his second booking of the game.
Chris Smalling should have done better with a close-range header, but the Reds failure kill off the depleted visitors- coupled with the narrow nature of the lead- began to turn into nervous tension around the ground.
Van Gaal introduced Fellaini (available for Europe despite serving a domestic suspension) and the giant midfielder came up with what could be the decisive, pivotal moment in the tie when he nodded in a superb cross from Memphis with the final play of the game to put the Reds in a strong position ahead of next week's second leg.
United Faithful Man of the Match: Memphis Depay
Overall team performance: 8/10