Marcos Rojo and Daley Blind were handed starting berths by Van Gaal, while Radamel Falcao, who moved to Old Trafford on a season-long loan from Monaco on transfer deadline day, also made his debut as a second-half substitute.
However, the show was stolen by another new recruit as Angel Di Maria delivered a wonderful display on his maiden home outing for United.
Di Maria opened the scoring with his first goal in a United shirt midway through the opening half before playing a part as Ander Herrera and Wayne Rooney made the points safe before half-time.
Rooney's strike made him the joint-third top-scorer in Premier League history with 175 goals, and United, using a back four for the first time in the Premier League this season, pulled further clear when the excellent Di Maria set up Juan Mata for a fourth after 58 minutes.
Falcao's arrival in the 67th minute did not prompt the final flurry that United fans would have perhaps wanted, but there is now likely to be a renewed belief that the club can challenge at the top of the table following last season's disappointing seventh-place finish.
United, whose emphatic triumph ensured QPR defender Rio Ferdinand endured a miserable return to his former club, made a fast start to proceedings and threatened in the seventh minute when Mata shot well over the crossbar from the edge of the area.
QPR, with Sandro and Niko Kranjcar in their team for the first time since the duo's deadline-day moves, appeared to have weathered the storm as some of the early intensity vanished from United's play, but in the 24th minute Van Gaal's men found the breakthrough their dominance of possession merited.
Clint Hill was penalised for a foul on Herrera and visiting goalkeeper Robert Green was beaten as an inswinging free-kick from Di Maria evaded everyone and crept into the bottom-left corner.
United had clear control of the encounter but Harry Redknapp's side were almost gifted an equaliser in the 31st minute by David de Gea.
The Spaniard rushed off his line in an attempt to clear a long ball forward and was grateful for a diving block from Jonny Evans that prevented Matt Phillips from scoring.
QPR were given a mountain to climb 10 minutes before half-time when former Athletic Bilbao man Herrera drove a low strike beyond the despairing Green to double United's lead.
Di Maria was heavily involved in the goal, surging down the left wing before slipping a neat pass into Rooney, who laid the ball off for Herrera to open his account after the England striker had seen his initial shot blocked.
Rooney effectively ended the game as a contest in the 44th minute, rounding off a neat move involving Herrera and Mata with a powerful finish.
Redknapp threw on Armand Traore for the unimpressive Hill at half-time and the move almost paid instant dividends as the substitute pulled the ball back for Kranjcar to bring a fine save from De Gea.
Yet QPR could not prevent United adding further gloss to a superb display. A cross-shot from Di Maria cut out three players and left Mata with the simple task of firing high into the net from close range.
Falcao was brought on to rapturous applause from the home supporters, yet it was one of QPR's debutants that almost cut the deficit, substitute Eduardo Vargas firing narrowly wide after being played through down the right-hand side.
A glittering showing from Di Maria came to an end as he was withdrawn with an apparent case of cramp before the Old Trafford crowd were denied a fitting finale to an encouraging afternoon when Falcao was thwarted by Green, who also saved from replacement Adnan Januzaj in the 90th minute.
