Goals from Juan Mata, Wayne Rooney and Zlatan Ibrahimovic were more than enough to overcome the Cherries, who could only muster a late response from Adam Smith. But how did the United players fare individually?
Goalkeeper and defence
David De Gea - 7
Commanded his penalty area smartly, and played the ball out with his feet brilliantly as per usual. There were large swathes of the game where De Gea could scarcely get a kick of the ball, but was alert on those rare occasions when it did come his way. Was unfortunate not to keep a clean sheet--his defense was slack to give Smith a chance to get his strike away, and De Gea could do nothing with the shot. Made a terrific save from Andrew Surman late on, and another just seconds later as Benik Afobe attempted to round him. A good beginning for the Spaniard.
Luke Shaw - 7
Defended wisely throughout, showing the vastly increased maturity that was beginning to show last season before his horrific injury. A couple of slack touches, particularly one which nearly let Bournemouth in during the first half, showed the rustiness he still needs to work through. However, his runs to overlap Anthony Martial only got better as the game went along. That partnership looks like it will only get better as the year goes along.
Daley Blind - 8
While Louis Van Gaal was occasionally derided last term for persisting with Blind at center back, it is clear that the Dutch international learned a fair bit. His reading of the game was superb, he distributed the ball to near perfection and cut out several dangerous Bournemouth attacks. Did brilliantly in the 57th minute to stop Jordan Ibe dead in his tracks when it looked certain the former Liverpool man would be in on goal. Strong performance.
Eric Bailly - 7
There is no denying Eric Bailly's athletic gifts: he's quick, skillful on the ball, strong and looks commanding in a penalty area. He reads the game and passes terrifically. However, he also has all the hallmarks of a young defender: he is often overenthusiastic when going into a tackle, and has a penchant for getting into a spot of trouble with referees. He'll be a joy to watch develop but will pick up some needless cards along the way.
Antonio Valencia - 7
Valencia was impressive in preseason and carried over his form from July and early August into the league. Did a good job of keeping Ibe under wraps throughout, and his crossing was a constant threat. Combined terrifically with Ander Herrera and Mata on a flowing move in the first half that wound up creating a chance for Rooney. If he and Shaw are to be Mourinho's first choice backs, then United will undoubtedly play with terrific width.
Midfield and attack
Marouane Fellaini - 6
It's interesting that - counting the Community Shield - United have now played two competitive games and Fellaini has started both. Mourinho seems to value his combative nature in midfield, but it also seems unlikely that he'll be starting on a week-to-week basis once Paul Pogba can be inserted into the lineup. The Belgian kept Bournemouth from developing any passing rhythm, particularly in the game's opening 20 minutes when the Cherries were probably the better side.
Ander Herrera - 7
The Spaniard showed once again why he is a crowd favorite at Old Trafford. His close control is something to behold, as is his passing range. Made a couple of incredible passes to find Valencia down the right wing, and his range will have to have impressed his new gaffer. Herrera will be hopeful that he can nab down a regular place in the starting XI this term, something he's been unable to do the last two years.
Wayne Rooney - 7
Rooney showed some rustiness, most notably in his first pass of the afternoon, which appeared to be intended to put Martial in behind the Bournemouth defense. It instead split Martial and Shaw, forcing both to tear off after it in an effort to keep the ball in play. As per usual with the United captain, there were a couple of poor first touches to go along with some lovely crossfield balls. Should have beaten Artur Boruc early in the second half when played in behind by Ibrahimovic, but did brilliantly to make it 2-nil to United in the 59th minute. The captain should be pleased with his performance.
Juan Mata - 7
It's clear that the man who was forced out of Chelsea by Mourinho is absolutely desperate to impress his manager this time around. Mata was smart in possession and linked the play well when cutting in from the right wing. It's evident that he is loathe to the stay out on the wing, which may not go over well with his manager but could bode well if Valencia continues to get down the wing the way he did on Sunday. Mata's goal was not the prettiest he has ever scored, but it was earned out of pure determination. If nothing else, that should please Mourinho.
Anthony Martial - 7
The Frenchman had slightly less success when running with the ball at his feet than he may be used to, but he was still credited with two assists. While it may be debatable whether he should have been, Martial's performance was good. He is expected to add width and pace, which he certainly did. The burgeoning partnership with Shaw does nothing but bode well for the future.
Zlatan Ibrahimovic - 8
The Swede stole all the headlines with his performance on Sunday. He had no shortage of Eric Cantona-esque flicks and tricks, and his goal was terrifically taken. Should have had an assist for an incredible half turn and flick that set Rooney in behind early in the first half, and had a free-kick brilliantly saved by Boruc soon afterward. The striker will drift in and out of games, as he did on Sunday, but when he is in them, he's an absolute match-winner.
Henrikh Mkhitaryan - 6
The Armenian showed just enough in his cameo to get supporters excited to see more. He was only given 15 minutes on the field but showed off the array of skills he has just before stoppage time began when he brought the ball out of the air before nutmegging two Bournemouth players. A solid display.
Morgan Schneiderlin - NR
The midfielder came on with less than 10 minutes on the clock to shore things up defensively. No great moments, no poor moments--did his job for the team.
Memphis Depay - NR
Had even less time on the pitch, coming on for Rooney in the 89th minute. Had a nice moment in stoppage time when he pinched the ball off of Francis and sent in a decent cross. He'll be hoping to be given more of a chance to impress soon.