New signing Angel di Maria was outstanding throughout, scoring the first before Wayne Rooney and fellow new boy Ander Herrera made the result a formality before the break and Juan Mata completed the rout in the second half.
When Radamel Falcao, on loan from Monaco, was introduced for the last quarter of the match for his debut, he joined Robin van Persie, Rooney and Di Maria in a potentially thrilling quartet which set the home crowd abuzz.
United's first win in four Premier League matches took them up to ninth place in the table, only two points outside the top four - a position that some critics have predicted will be beyond them again after finishing seventh last season.
Although Rangers provided feeble opposition, there was the promise of better things to come from United, given their enviable range of attacking options.
"We played much, much better," Spaniard Mata told Sky Sports afterwards. "Hopefully it's the first step of a good run of results."
Van Gaal, who also gave debuts to defender Marcos Rojo and midfielder Danny Blind, enjoyed the crowd's applause as he left the pitch following a first victory as manager after a difficult start which included a League Cup defeat at third tier MK Dons.
"It's a very good start. I said before the game 'let's make a new start'.
Reminded that after taking over as manager of Bayern Munich he did not win until the fourth game, then won the league, he responded: "Maybe it's a good signal".
It all added up to a forgettable return to Old Trafford for QPR centre-half Rio Ferdinand, who played for United for 12 years until last May, winning six Premier League titles and a Champions League final.
He received a presentation before kickoff from the United director Bobby Charlton but once the game started was soon under pressure, being forced into a hurried clearance to deny friend and former England team-mate Rooney.
In the 24th minute Ferdinand was as helpless as the rest of the visitors' defence when Di Maria flighted a perfect free kick that bounced once and flew past goalkeeper Rob Green.
Di Maria said afterwards that he had meant to score, having practiced the same free-kick in training.
There was a rare alarm for the home side when Matt Phillips had his shot blocked by Jonny Evans with goalkeeper David de Gea out of position but by halftime United had two more goals.
In the 35th minute Di Maria's run allowed Rooney to cut the ball back for Herrera to drive low into the bottom corner of the net and nine minutes later Rooney found the same spot after a smooth passing move.
Ferdinand was badly embarrassed for the fourth goal after 58 minutes when Di Maria's cross bypassed him and Mata lifted a shot over the goalkeeper.
For the London side it was a second heavy away defeat following their 4-0 loss in the local derby at Tottenham Hotspur and a third defeat in four league games this season, leaving them in the bottom five.