Van Gaal handed debuts to Daley Blind, Marcos Rojo and Radamel Falcao as the new-look side seized control early on.
Angel Di Maria opened the scoring on 24 minutes when his curling free kick evaded everyone and found its way in at the far post, and Ander Herrera — making his first appearance since the opening-day defeat to Swansea — added a second soon afterwards on his return from injury.
Wayne Rooney fired home a well-taken third just before the break, and Juan Mata made it four just before the hour-mark with a confident finish.
Falcao, who started the game on the bench, replaced Mata on 67 minutes and came close to opening his account when Rob Green spilled a Blind shot, but the QPR keeper reacted quickly to deny the Colombian.
Van Gaal, who had gone four games without a win, will want to use this victory as a springboard for the rest of the season. This certainly felt like the start of a new era at Old Trafford.
United, playing in a 4-4-2 diamond, passed the ball quicker, they were more clinical in front of goal and the atmosphere inside the ground was jubilant.
With 150 million pounds of new talent available to him, and players like Mata, who had an outstanding game, Van Gaal has the potential to achieve a top-three finish, as outlined by his employers, at the very least.