All three impressed, but it was the contribution of Di Maria which perhaps deserves the greatest praise.
The Argentinian gave United fans a glimpse of his potential in the drab 0-0 draw at Burnley two weeks ago, but on his home debut he was simply irresistible.
The B150million 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.
Despite the public excitement surrounding the arrival of Falcao, Rio Ferdinand received the biggest reception from the home fans before kick-off.
The former United centre-half, who complained he was not given a proper send off in the summer, received a huge ovation as well as a present from Sir Bobby Charlton just before kick-off.
After the first whistle sounded, it did not take long for Ferdinand's old team-mates, and United's new signings, to put him under immense pressure.
Mata raced down the left and whipped in a perfect ball for Rooney, but mis-controlled and Ferdinand hooked the ball clear.
Van Gaal wrote in his pre-match notes that he was worried about nervousness gripping his players at Old Trafford, but that was certainly not the case on Sunday.
United passed the ball quickly and confidently, and they tested the away defence with a series of teasing crosses.
Herrera pulled the ball back to Mata after a clever nutmeg from Rafael, but the former Chelsea man skied his shot.
Down the left, Rojo lobbed the ball to the back post where Herrera cocked his right leg back ready to fire a volley at goal, but Van Persie clumsily nicked the ball away from the Spaniard.
With so much pressure on them, it only seemed a matter of time before QPR conceded, and they did in the 23rd minute.
After a needless foul on Herrera by Clint Hill, Di Maria whipped a curling ball over the heads of four players and the ball drifted in past Robert Green at his far post.
Within a few minutes of Di Maria's first United goal, the hosts almost handed QPR a route back into the match. David De Gea, usually such a calm operator, raced out of the box trying to clear a long punt up field from Niko Kranjcar. The goalkeeper failed to communicate with Jonny Evans and the ball fell to Matt Phillips, but he failed to turn the ball into the empty net and United's fans breathed again.
Those same fans were up on their feet moments later when United moved 2-0 ahead.
Once again Di Maria played an important part, racing 50 yards down the left before playing Rooney in with a lovely pass between two defenders. The striker's shot was blocked, but he then squared to Herrera, who drilled the ball past Green.
The Stretford End demanded United attack and they did. Just before half-time Rooney made it 3-0.
Herrera played a delicious one-two with Mata and he touched the ball off to Rooney, who powered a low shot past Green.
QPR boss Redknapp replaced Hill with Armand Traore at half-time and the former Arsenal defender made an immediate impression, driving at the United defence with a long run. He squared to Kranjcar, who shot at goal, but De Gea stuck his right foot out just in time.
A large number of United fans rose to applaud Falcao as he warmed up on the touchline. Those whose focus remained on the game watched United bag a fourth.
Di Maria adventurously attempted a 25-yard effort which instead landed straight at Mata's feet. The Spaniard, three yards clear of his nearest marker Ferdinand, tucked the ball past Green from 10 yards.
Falcao came on with 23 minutes to go to link up with Rooney and Van Persie in a devastating front three.
United's defensive vulnerabilities were highlighted when Tyler Blackett moved aside to allow Eduardo Vargas to shoot on goal, but he dragged his effort wide.