The visitors took the lead on 28 minutes through Ki Sung-yueng before Wayne Rooney got United level early in the second half.
However, Swansea made sure of the points with around 15 minutes left thanks to a strike from Gylfi Sigurdsson.
Read Sports Mole's minute-by-minute report below to find out how all of the action unfolded at the Theatre of Dreams.
11.47amDidn't sleep last night? Me neither. THE PREMIER LEAGUE IS BACK! It's been a fantastic summer with the World Cup and all, but nothing quite beats the thrill of the domestic campaign. The 2014-15 season gets underway today with Manchester United hosting Swansea City at Old Trafford and we'll be here for the next few hours to guide you through all of the action.
11.54amSo, Louis van Gaal's first competitive game as Manchester United boss sees him pick an untried starting XI. Debutants Jesse Lingard and Tyler Blackett are both included, while new signing Ander Herrera is handed a place in the midfield. Newly-named captain Wayne Rooney joins Javier Hernandez up to, with Juan Mata playing just behind.
12.04pmSwansea boss Garry Monk has made a total of eight new signings this summer, though only two of them are in his starting lineup this afternoon. Lukasz Fabianski and the returning Gylfi Sigurdsson are in, but Bafetimbi Gomis and Jefferson Montero have to settle for places on the bench.
12.07pmMan Utd captain Wayne Rooney talking to BT Sport about Louis van Gaal: "He's been great for us all. He's come in, he's an honest person, you can see he's a fantastic manager. We're trying to play a new system and we've done it quite well in pre-season. But today's where it starts - the first game where we have to go out and we have to win. We're really looking forward to it so hopefully we get a good result."
12.11pmMore from Rooney: "We all obviously help each other. Things that get said in the dressing room we'll keep in there. We all know how much of an important season this is for us. Today's the start of that and it's vital we get three points. Today's about the team. It's an important game for us, obviously the first of the season, and we want to get off to a good start and hopefully get three points."
12.16pmIt's worth pointing out that Man Utd started last season against Swansea, earning a 4-1 win at the Liberty Stadium. However, things went from bad to worse after that as David Moyes struggled to get to grips with life at Old Trafford. Those days might seem a long time ago, but the United players will be desperate to get out that a put the last campaign to bed once and for all.
12.19pmWhile last season was a disaster for Man Utd, Swansea faced some tough moments as well before securing their survival. It looked as if Garry Monk's side might be involved in a relegation battle, but they managed to climb out of it towards the final few weeks of the campaign to finish in 12th place in the table.
12.24pmThere are sure to be plenty of eyes on the 3-5-2 system that Louis van Gaal is employing today, and it would be fair to say that Swansea probably fancy their chances looking at the Man Utd back three. Jones, Smalling and Blackett doesn't exactly scream authority, does it? With just over two weeks remaining in the summer transfer window, you would expect Van Gaal to bring in a top-quality centre-back before deadline day.
12.28pmSpeaking of Man Utd's transfer policy this summer, Paul Scholes has recently had his say on the matter. The former midfielder believes that the team is "crying out" for quality midfielders. You can read what he thinks Van Gaal needs to do to strengthen here.
12.31pmMan Utd may be struggling in the transfer market, but Swansea haven't been this summer. Garry Monk has brought in eight new faces to his squad, with a fair bit of quality among those additions. Lukasz Fabianski is certainly a fine replacement for Michel Vorm in goal, while the likes of Bafetimbi Gomis, Gylfi Sigurdsson and Jefferson Montero have demonstrated that the club is still as ambitious as ever, despite last season's stuttering campaign.
12.37pmJust under 10 minutes to go until kickoff. If you've got a spare couple of minutes, why not check out our video preview of this afternoon's match?
12.40pmStating the obvious a bit here, but it's pretty much a full house at Old Trafford today. The fans are nearly all in place as we await the teams.
1 minKICKOFF! The teams are out, the pre-match handshakes have been done, and it will be Swansea to get us underway as the 2014-15 Premier League season officially begins. Here we go!
4 minIt's been the home side who have enjoyed the better start, seeing plenty of the ball during the opening few minutes. Man Utd carve open a half-chance when Mata and Rooney combine, though the latter is denied when Fabianski comes off his line to gather the ball.
7 minYou can see already that Man Utd could leave themselves a bit exposed with three at the back. Swansea almost cause the hosts a problem when the ball is played through to Routledge, but his first touch is a poor one that allows De Gea to quell the danger. Garry Monk's side don't look particularly daunted.
10 minMan Utd debutants Blackett and Lingard have given a good account of themselves so far. Lingard in particular has looked lively down the right wing. The youngster almost catches out Fabianski at his near with a cross before whipping in another cross that just evades Hernandez.
12 minCHANCE! First proper opportunity goes Swansea's way as Sigurdsson tries his luck from 25 yards. His effort dips and moves in the air a bit, but De Gea does enough to get down and make the save. Rooney goes up the other end moments later, only for Fabianski to gather his tame effort.
15 minSwansea are having a pretty good spell at the moment. As mentioned previously, the visitors are looking confident when in possession, using the ball well to attack their opponents. However, they're not doing a great deal to get in behind Man Utd.
18 minIt's been a fairly physical start to this match so far. There have been one or two robust challenges from both sides, especially in and around the midfield area. Man Utd new boy Herrera certainly looks like he can look after himself, even though he has something of a diminutive frame.
21 minSome concern for Man Utd as Lingard stayed down after challenging for the ball. It might have been an ankle problem for the youngster. However, he is back on after receiving treatment for a brief moment on the touchline.
24 minSUBSTITUTION: Actually, Lingard isn't okay. He played on for a few minutes, but now he is being withdrawn. Adnan Januzaj, Man Utd's new number 11, is the man who replaces him.
25 minCHANCE! Close for Man Utd! Jones bombs down the right wing before seeing his cross take a deflection and nearly creep in at the near post. The hosts get a free kick soon after that Mata takes, but his shot is beaten away by Fabianski.
26 minYELLOW CARD! The first booking of the season goes the way of Swansea's Dyer for a tasty challenge on Januzaj. The visitors aren't happy with the decision from referee Mike Dean and you can see why. It looked like a fair tackle from here.
28 minAre Swansea about to spoil Man Utd's party? The visitors have taken the lead thanks to a well-take goal from Ki Sung-yeung. The ball fell to the Korean on the edge of the box and he kept his head to fire the ball low into the bottom corner, out of the reach of De Gea. There's suddenly a different atmosphere inside Old Trafford.
31 minThat goal has sparked Man Utd into life a bit, though it must be said that it's been an underwhelming start to the season from the Red Devils. Mata and Rooney aren't seeing enough of the ball for the hosts, while Swansea have been organised and disciplined.
36 minThere are sure to be a few Man Utd fans out there who are having flashbacks to last season under David Moyes. However, there is still plenty of football left to be played in this match. Louis van Gaal won't be panicking just yet, though he is probably thinking that one or two tactical changes need to be made at half time. Shinji Kagawa and Nani are among the players available on the bench.
39 minOne area of encouragement for Man Utd is that Januzaj has made a bit of a difference since coming on. The young Belgian is having a good old battle with Swansea full-back Taylor down the right side. Meanwhile, an area of concern for Swansea is that they're losing their discipline a bit. The visitors have given away a few needless free kicks.
42 minChants of "Attack! Attack! Attack!" ring out around Old Trafford as the Man Utd fans try to spur their team on. The hosts are showing a bit of attacking intent as we head towards the final few minutes of the half, but there's still an element of flatness to what they're doing. It's just not happening for the Red Devils at the moment.
45 minThree minutes of added time at the end of the first half...
1.41pmAnd what about Swansea? Well, Garry Monk has every reason to be pleased with his side's performance so far. The visitors have been organised and well-drilled. They could well be expecting a bit of a barrage from the home team after the break, but they will certainly be fancying their chances.
1.44pmA word on Ki's goal: the Korean was afforded way too much time on the edge of the Man Utd box to get his shot away. The midfielder was not picked up by anyone, allowing him to find the bottom corner with relative ease.
46 minSECOND HALF UNDERWAY! The players are back out and it'll be Man Utd to kick us off for the second half. Can Louis van Gaal's side turn things around in the next 45 minutes? The hosts have made one change during the interval with Nani replacing Hernandez.
48 minYELLOW CARD! An early booking at the start of the second half for Swansea full-back Taylor after hacking down Januzaj down the right side.
51 minIt's been a positive start to the second half for Man Utd. They've seen plenty of the ball during the opening few minutes, while Swansea have barely been outside of their own half. Interestingly enough, Van Gaal has switched to four at the back, with Young moving to left-back.
52 minMan Utd are level thanks to a superb volley from Rooney! Mata's corner wasn't cleared, and there was the captain about six yards out to find the net with an acrobatic strike. Old Trafford erupts. Meanwhile, Swansea have made a change with Tiendalli replacing Taylor.
54 minYELLOW CARD! Another booking for Swansea now as Shelvey is cautioned for fouling Mata and then booting the ball away. Silly stuff from the Swansea midfielder.
57 minAs you might imagine, the mood inside Old Trafford has completely changed following Rooney's equaliser. There's an added spring in the steps of the players as well. This is going to be a big test for the visitors because they're probably going to be bombarded for the next 30 minutes or so.
60 minSwansea are being given very little time on the ball at the moment as Man Utd press for an equaliser. Mata and Rooney are much more involved now, whereas the were largely ineffective during the first half. Januzaj is the latest Man Utd player to have a crack at goal following a darting run into the Swansea box, but the young Belgian can only curl the ball high and wide over the cross bar.
63 minLouis van Gaal is sure to have plenty of criticism for his team's performance, but the Dutchman is likely to be pleased with how his players have equipped themselves in the second half.
67 minCHANCE! Almost another goal for Rooney, and what a strike it would have been! The Man Utd skipper tries his luck with a free kick from 25 yards, but his effort goes inches wide of the post. Meanwhile, both teams have made changes. Fellaini enters the action in place of Herrera for the hosts, while Montero is introduced for Dyer.
70 minTwenty minutes left to play at Old Trafford and it's the hosts who are looking the more likely to score right now. Swansea continue to toil for possession, but they're not seeing much of the ball at all. That said, they remain on course to come away from here with a point.
72 minUnbelievable! Swansea might not have seen too much of the ball during this second half, but they are back in front thanks to Gylfi Sigurdsson! Montero's cross from the left was met by Routledge, who scuffed his shot, but there was Sigurdsson inside the box to fire low past De Gea. Amazing.
75 minNow it's Swansea who are looking rejuvenated. Man Utd have around 15 minutes of normal time left to get something out of this game. This is certainly not the start that Louis van Gaal was expecting.
77 minSUBSTITUTION: Swansea's last change sees Gomis replace Bony, who has worked his socks off this afternoon in that lone striker role. For those who are interested, Man Utd haven't lost at home on the opening day of the season since 1972. Is that all about to change?
81 minWhat a tackle from Jones! Gomis played a one-two before going clear through on goal, but Jones was just about able to get back and make a last-ditch challenge on the substitute. Following that, Ki goes into the book for a clash with Jones.
83 minYELLOW CARD! Now it's the Man Utd youngster Blackett who is cautioned after a strong challenge on Gomis. The Swansea striker has ruffled one or two feathers since he came on. Not surprising considering the size of him.
85 minSomething of a half-chance for the hosts as Young has a go from 25 yards, but Fabianski is able to get down a make a simple save. Time is running out for Louis van Gaal's side. Five minutes plus stoppage time left to play.
88 minSwansea are doing just about enough to keep Man Utd at bay as we enter the final few minutes. Hats off to Garry Monk's side - they've been impressive this afternoon. If they can hang on for the remainder of this match then they will have themselves a sensational start to the season.
90 minThe fourth official indicates that there will be FOUR MINUTES of added time. Will that be enough for Man Utd to get something out of this match?
90+2 minNothing doing for Man Utd at the moment. They'll be very pleased to see Robin van Persie back in action because there's been very little urgency in their attacks today.
2.41pmMike Dean blows the full-time whistle, signalling a losing start to the season for Man Utd. Swansea have come away with a 2-1 win thanks to goals from Ki and Sigurdsson. This was not what Louis van Gaal had in mind when he took over at Old Trafford earlier this summer. The Dutchman already has a lot to think about.
2.43pmThat's all from our live text coverage of today's game, but you can keep up to date with all of the post-match reaction from both camps when it comes in on Sports Mole. Thanks for your company and we hope to see you again soon. Goodbye!