British record signing Angel Di Maria showed his class and settled early United gitters when his free kick crept past Robert Green for the first goal.
Ander Herrera drilled in soon after and Wayne Rooney’s sharp finish all but ended the contest before half time.
Juan Mata joined the party thanks by steering in a Di Maria shot.
United’s last home game had finished with a very different mood around Old Trafford and Van Gaal’s starting line-up showed major changes from that loss.
New signings Di Maria, Daley Blind and Marcos Rojo were included from the start with Falcao starting from the bench.
Van Gaal forfeited his favoured 3-5-2 formation for a 4-4-2 formation; this was due to injuries to centre-back pair Phil Jones and Chris Smalling during the international break.
The changes fuelled an enthusiastic atmosphere among the home fans and QPR proved to be the right opposition for a confident win.
Mata, playing at the attacking tip of a midfield diamond, shot over from 20 yards, before Di Maria gave United a goal cushion to go with a lion’s share of the possession.
Di Maria floated a free-kick over its intended targets and, with goalkeeper Rob Green standing still in expectation of a tough, bounced inside the far post.
The visitors barely created opportunities for themselves taking the defensive approach, but if Johnny Evans hadn’t blocked Matt Phillip’s shot after David de Gea rushed out to try and halt a rare attack, they could have been level.
An audacious run from Di Maria drew the attention of drew away two defenders and when Rooney laid the ball into the path of Herrera, the Spaniard drilled a low shot into the bottom corner.
The third arrived soon after as the QPR defence stood off their men, allowing Mata and Herrera to exchange passes and Rooney the time to pick his spot inside the near post.
The introduction of Armand Traore improved QPR after the break, but Mata and Rooney’s over-elaboration with the goal at their mercy, and the rueful smiles that followed, summed up the exhibition pace of the second half.
Mata did not have to wait long for another chance – blasting home after Di Maria scoffed an ambitious effort into his path.
Falcao was introduced to loud cheers with a little over 20 minutes to go and was denied a golden opportunity by Green’s scrambling recovery save.
The Colombian’s new side should provide him with plenty more chances if they continue in the same vein, while QPR will need to go back to the drawing board if they want to survive in the top flight.