The Red Devils then sealed the points after the break when Juan Mata found the net.
Read Sports Mole's minute-by-minute report below to find out how all of the action unfolded at Old Trafford.
3.01pmGood afternoon and welcome to Sports Mole's live text coverage of today's Premier League encounter as Manchester United welcome Queens Park Rangers at Old Trafford. There's plenty of anticipation at the Theatre of Dreams as United look to record their first win of the season, and we will bring you the team news as soon as we have it.
3.03pmMAN UTD: De Gea; Rafael, Evans, Rojo, Blackett; Blind, Herrera, Mata, Di Maria; Rooney, Van Persie
3.06pmSo, there are starts for summer signings Marcos Rojo, Daley Blind, Ander Herrera and Angel di Maria this afternoon for Man Utd, while Luke Shaw and Radamel Falcao have to settle for places on the bench. Further changes for the hosts see Rafael and Jonny Evans return to the defence.
3.13pmQPR boss Harry Redknapp has made two changes to his starting XI following the team's 1-0 win over Sunderland before the international break. Sandro comes in to make his debut for the club, while Niko Kranjcar makes his first appearance of the season after returning to Loftus Road for a second loan spell earlier this summer. Joey Barton and Jordon Mutch are the players who make way through injury.
3.16pmMan Utd manager Louis van Gaal: "The fans shall expect a new start of course, but we have to build up a new hierarchy and that always needs time. We've done very well in the transfer market. That's a big plus, and we have to produce results, starting against QPR."
3.20pmQPR captain Clint Hill: "We know we'll be massive underdogs, but that might just suit us. All the pressure will be on them, make no mistake about it. There will be a level of expectancy amongst the United fans, especially after the business they've done in the last few weeks.
"They've not had the best of starts to the season and they're yet to win, so that might be playing on their minds as well. We'll be heading there full of confidence and with the signings we've made, who knows what might happen."
3.23pmOf course, today holds plenty of significance for Rio Ferdinand, who return to Old Trafford for the first time following his summer departure from Man Utd. The defender won a glut of honours during his 14 years with the Red Devils, including six Premier League titles and the Champions League. Despite having such a deep association with the club, the former England international has made it clear in the build-up that he is here to win with QPR this afternoon.
3.29pmIf you have a few minutes to spare before kickoff, why not check out or video preview of this afternoon's match?
3.33pmHEAD TO HEAD: As you might expect, Man Utd have the better record when it comes to past meetings between these teams, winning 30 games compared to just six for QPR. Meanwhile, there have been 12 draws. For the record, the R's have never beaten United at Old Trafford in the Premier League.
3.36pmQPR's last visit to the Theatre of Dreams back in November 2012 saw them lose 3-1, while the reverse fixture at Old Trafford saw United run out 2-0 winners. That game was notable for the fact that it produced Ryan Giggs's last goal in a United shirt.
3.39pmFormer Man Utd defender Rio Ferdinand: "In pre-season, I was really excited for Man United. They looked really fit and decisive and they had a good understanding of the system. It was almost like a complete reversal when the season started. I think they'll get it right.
"I think the manager who's there now gets things right. I have every confidence he'll bring back good times at Man United, it's just a matter of how long."
3.45pmAs you might expect, there's an incredible sense of anticipation around Old Trafford this afternoon. It's hard to see beyond a Man Utd win, but let's not forget that QPR have some tidy players at their disposal. Leroy Fer, Junior Hoilett and Sandro are sure to give the hosts a few things to think about this afternoon.
3.51pmRio Ferdinand has already received a great ovation from the Old Trafford faithful after leading QPR out for their warm-up, but he'll know full well that there is no room for sentiment once that whistle goes. The players are due to emerge in the tunnel any moment now.
3.56pmThe teams are in the tunnel, and there are plenty of focused-looking faces among the two sides. Wayne Rooney stands at the front of the Man Utd line, while Clint Hill is there leading the way for QPR. Kickoff is just minutes away.
1 minKICKOFF! The teams are out, the pre-match handshakes have been done, and it will be QPR to get us underway. Can the hosts earn their first win of the season, or will the visitors spoil the party? We're about to find out.
3 minIt's been a positive start from the hosts, who are looking to attack the away side instantly. Di Maria has already seen a bit of the ball down the left flank, while Blind is busy ferreting around in midfield. QPR are needing to be focused from the off.
6 minIt's still Man Utd who are dictating the early pace of this game with some crisp passing and fluid movement. The hosts win a corner thanks to some good work from Rafael down the left side, but the resulting kick from Di Maria is too deep and goes out of play for a goal kick.
7 minCHANCE! An early opening for Man Utd sees Rafael and Herrera linking well down the right before the latter feeds Mata on the edge of the box. The Spaniard hits it first time, only to see his effort sail over the crossbar.
10 minQPR have hardly been out of their own half during these opening 10 minutes. They're having to sit very deep as Man Utd surge forward again and again, though the hosts haven't made their dominance count so far. Still, this is looking a bit ominous for Harry Redknapp's side.
13 minThe pace has been slowed down by Man Utd in the last few moments, with players such as Blind and Herrera happy to just knock the ball about in midfield. Despite taking their foot off the gas ever so slightly, the home side are still in full control of this match.
16 minCHANCE! Close to an opening goal for Man Utd there as a cross from the left looks to be heading towards Herrera inside the QPR box, but Van Persie get in his teammate's way at the last moment, allowing the visitors to survive. It looked as if there was a lack of communication there between the striker and the midfielder.
20 minQPR are beginning to assert themselves a bit more now, with Austin getting more service up front. Fer and Sandro are getting stuck in around the midfield area, letting their opponents know that they're about. Still, it's Man Utd who are looking far more dangerous at the moment. They're just lacking that bit of incisiveness in attack.
23 minIt's not the most orthodox of goals, but Angel di Maria gives Man Utd the lead on his home debut for the club! The Argentine whips a free kick into the box from the right side of the pitch, but it somehow evades everyone before hitting the back of the net. We've seen those type of goals before.
26 minPENALTY APPEAL! Man Utd really have their tails up now. Herrera and Mata link on the edge of the box before the former goes down after a collision with Hill. Referee Phil Dowd has a look at it before telling the Spaniard to get up. In fairness, that would have been harsh had it gone against Hill.
29 minDi Maria is really enjoying himself out there this afternoon. The winger is always looking to go forward whenever he is on the ball, using that trademark pace of his to leave QPR shirts in his wake. Harry Redknapp will be anxious to come up with a better game plan to keep the £59m man quiet.
31 minCHANCE! QPR almost level in bizarre circumstances as De Gea comes out to gather the ball, but gets nowhere near it. Phillips is there to pounce, prodding the ball towards goal, only for Evans to slide in and block the shot.
32 minYELLOW CARD! The first booking of the game goes the way of Van Persie for a cynical foul on Hoilett just as QPR were looking to break down the left.
35 minDespite going behind, QPR are enjoying a decent spell of possession. They're starting to show a bit more confidence going forward, though it's clear that they're lacking a bit of quality in the final third. Still, Harry Redknapp will be encouraged by what he's seen in the last few minutes.
36 minMan Utd extend their lead through Ander Herrera, but that goal was all about Di Maria. The winger made a brilliant run down the left from inside his own half before feeding Rooney. The captain's initial effort is blocked before he finds Herrera, who fires into the bottom corner from the edge of the box.
39 minJust over five minutes to go until half time, and Man Utd are really enjoying themselves out there now. The home fans are encouraging them to bomb forward at every opportunity, which the players are duly doing. QPR will be keen to keep their opponents from scoring a third before the break, otherwise it could well be curtains.
42 minMan Utd come close to grabbing a third as Di Maria floats a pass in towards Rooney, but the United skipper just can't reach the ball. An inch or two nearer his boot and he would probably have poked that beyond Green.
43 minWhat a great goal that is from Wayne Rooney to give Man Utd a commanding 3-0 lead! Rooney, Mata and Herrera all combine around the QPR box before the Man Utd captain strikes a sweet shot low into the bottom corner. QPR just could not deal with the home side's passing and movement there.
4.50pmReferee Phil Down blows the half-time whistle, bringing an end to a blistering opening 45 minutes for Man Utd. New signings Di Maria and Herrera put the hosts 2-0 up before Rooney got in on the act. It's been a dominant display so far from Louis van Gaal's side. Meanwhile, this match is now an exercise in damage limitation for QPR.
4.53pmThe undoubted start of that first half was Di Maria, who terrorised the QPR with his pace. The Argentine looks like just the player that Man Utd need thanks to his direct style of play. The visitors must already be sick of the sight of him.
4.59pmWith Man Utd in such a comfortable position, Louis van Gaal must be thinking of introducing Radamel Falcao at some point in the second half. The manager probably doesn't want to put too much pressure on the striker, so this is the perfect scenario.
5.02pmAs for QPR, Harry Redknapp has a real job on his hands to lift his players for the second half. The away dressing room must be a depressing place at the moment following that first-half mauling. A goal early in the second period might give Man Utd something to think about, but it's a long way back for the newly-promoted side now.
46 minSECOND HALF UNDERWAY! The teams are back out and it will be Man Utd to kick us off. QPR have made a change during the interval, with Armand Traore replacing Clint Hill.
47 minCHANCE! QPR almost reduce the deficit through Kranjcar, but De Gea is there to make the save. Traore did brilliantly there, running at the Man Utd defence before teeing up his teammate on the edge of the box. Kranjcar's effort is a low one, though the Spanish goalkeeper does well to keep it out with his foot.
50 minCHANCE! Now it's Man Utd who come close to finding the net as Mata finds Rooney in the box, but the ball gets stuck under his feet and Green gathers.
53 minFollowing that early opening for Kranjcar at the start of the second half, Man Utd have seized control of this match once more. Blind in particular is impressing in midfield, stopping QPR from getting forward and setting his team away at the other end.
57 minDi Maria is involved again as Man Utd make it 4-0 through Juan Mata! Di Maria's scuffed shot from the edge of the box finds its way to the Spaniard, who takes a touch before smashing the ball past Green and into the roof of the net from about eight yards. Meanwhile, QPR make a change as Charlie Austin is replaced by Eduardo Vargas.
60 minAn hour played at Old Trafford and the Man Utd fans are in party mode. Falcao has just warmed up down on the touchline, getting a big ovation in the process. How long before we see the Colombian striker?
63 minRooney tries to curl a speculative effort into the corner from 25 yards, but his effort sails high over the crossbar. Di Maria then feed Van Persie with a floated ball over the top that the striker hits into the hands of Green. The Man Utd players are really enjoying themselves out there at the moment, with everyone getting involved in attack. QPR can only sit back and try to soak up the pressure as the hosts look for a fifth goal.
66 minSUBSTITUTIONS: Here comes Falcao for Man Utd, replacing Mata with 25 minutes left to play. The number nine gets a rousing reception as he steps onto the pitch at Old Trafford. A second change for the Red Devils sees Valencia enter the action in place of Rafael.
69 minSome good play from Van Persie down the left ends with the striker's cross just evading a couple of red shirts waiting in the box. In fact, the Dutchman's cross just grazed the woodwork on its way through. Man Utd are showing no signs of letting up here, which is bad news from a QPR perspective.
73 minSUBSTITUTION: It's gets worse for QPR as Sandro is forced off with an injury. Karl Henry comes on in place of the combative Brazilian midfielder. Just over 15 minutes left to play at Old Trafford.
76 minFalcao hasn't caused QPR too many problems since he came on, though his movement has been good. The Colombian has a knack of losing his marker and getting into some decent positions inside the opposition penalty box. If this day was to get any better for the hosts, then a goal from Falcao would probably do the job.
77 minCHANCE! QPR are gifted a good opportunity to pull a goal back through Vargas, only for the substitute to drag his show wide of De Gea's post. The Chilean international was allowed a way through there following some confusion from Blackett, but he didn't have the precision necessary to find the net.
80 minA little bit of a worry here for Man Utd as Di Maria goes down clutching the back of his leg, though it just looks to be a touch of cramp that the Argentine is suffering from. It seems as if he'll be fine to continue for these final 10 minutes.
82 minSUBSTITUTION: Louis van Gaal clearly feels as if it would be too much of a risk to keep Di Maria on, so the winger is replaced by Adnan Januzaj for the final stages. The £59m has been superb this afternoon.
83 minCHANCE! That was the moment for Falcao to really make an impact, but he is denied by Green! Blind's long-range drive was parried away by the QPR goalkeeper, giving the Colombia the opportunity to score with the rebound. However, Green did well to react quickly and smother the shot.
86 minGroans of frustration come from the stands at Old Trafford as Valencia makes a good run into the box before seeing his tame pass to Rooney cut out by a QPR shirt. That was poor from the substitute. He had plenty of bodies to aim for in the middle.
88 minRooney tries his luck with a half-volley from about 25 yards that Green has no trouble in getting down to save. We're into the final minutes now at Old Trafford.
90 minSAVE! Green does well again to keep Man Utd out following a shot from Januzaj. The youngster arrived late in the box to hit a low effort towards goal, but the QPR goalkeeper was there to make a fine reaction save. Three minutes of added time are indicated by the fourth official.
5.53pmThe full-time whistle goes and Man Utd have their first win of the season thanks to a resounding 4-0 victory over QPR. Angel Di Maria, Ander Herrera and Wayne Rooney gave the hosts a commanding 3-0 lead at the break before Juan Mata sealed the points in the second half. Louis van Gaal is sure to be delighted with his side's display, while Harry Redknapp will be eager to get away from Old Trafford as soon as possible.
5.55pmThat's all from our live text coverage of this afternoon's match, but don't forget that you can keep up to date with all of the reaction from both camps right here on Sports Mole. Thanks for your company, we hope to see you again soon. Goodbye!