The victory was satisfying enough for the new manager, even if this was a victory achieved against a side who looked a shadow of the vibrant team that enjoyed its first season in the top-flight last year, and there was no shortage of other positives for Mourinho to focus on.
Most notable was the performance of two of his four high-profile signings with Zlatan Ibrahimovic continued his remarkable record of scoring on his league debut — the striker has now scored on his first appearance in La Liga, Serie A, La Ligue, the Champions League and the Premier League — and Eric Bailly looked impressively solid at the heart of the back four.
There were also a telling, if inconsistent contribution from Wayne Rooney, who added the second goal, while Juan Mata, restored to the starting line-up just a week after he was humiliated at Wembley after finding himself a substituted substitute, scored the important opening goal five minutes before half-time.
Adam Smith’s 69th minute reply for Bournemouth took some of the gloss off an improved second-half performance but with Henrikh Mkhitaryan, a second half substitute, and Paul Pogba yet to be integrated into the team, there was little to dent Mourinho’s belief his side are capable of challenging for the title.
“We don’t need to make a statement,” said the manager. “Everybody knows that we are going to fight for the title.
“Win it or not win it is a different story. We don’t hide in our words or our approach, so we are going to fight until it’s possible.
“If one day it’s not mathematically possible, then we’ll think about top four, which would be one step ahead of last season, which would be fine. But we want more than fine.”
A pedestrian first half offered more reminders of the unloved Van Gaal era than it offered a promise of a brave new world under Mourinho, with Rooney spurning the only clear chance before Mata latched onto a poor back-pass from Bournemouth’s Simon Francis and scored after benefiting from a second fortunate deflection off the defender.
The second half was much improved from United’s point of view with Ibrahimovic offering an effective focal point up front that brought Rooney into the game.
The United captain made up for another missed opportunity by heading the 59th minute second goal, following Anthony Martial’s mishit shot. Ibrahimovic killed off the game five minutes later with a well-placed shot from long range.
The Swedish international may be 34 but the initial signs are he will have a major influence on United’s season.
“At his table for breakfast and for meals he is surrounded by the young ones, the kids,” said Mourinho.
“Luke Shaw, Marcus Rashford, these are the guys who are with him at the table. He knows what he can be for them.
“But, for the team, you have to forget the passport, that he is 34.
“The body and mentality are not those of a 34-year-old guy. He’s at the top of his qualities.”
Rooney in particular had reason to be grateful for his new team-mate at the start of a season when his future in the team is far from certain. “I keep doing it, I’ve nothing to prove to anyone,” said the forward.
“I’ve played this game a long time. I believe I’m good enough to play every game and if I play in that position, I’ll score goals.
“You are always optimistic you can win titles, but I think the club made a statement with the signings and the new manager has won trophies wherever he has been.”
Bournemouth will have to improve quickly if they are to avoid a long relegation fight. The afternoon, though, belonged to Mourinho.
“When you look at the players who were not on the pitch, we have a lot,” he said.
“When September arrives with the Capital Cup and Europa League, we have the people to play and try and be competitive in every competition.”
Boruc 6; A Smith 6, Francis 4, S Cook 5, Daniels 6; Surman 6, Arter 6; Ibe 7 (Afobe 68,6), L Cook 6 (Gradel 81,6), King 6; Wilson 5 (Grabban 67,6). Not used: Federici, Gosling, Ake, B Smith.
De Gea 6; Valencia 8, Bailly 8, Blind 7, Shaw 6; Herrera 6; Mata 7 (Mkhitaryan 75, 6), Rooney 7 (Depay 89, 6), Fellaini 6, Martial 6 (Schneiderlin 85, 6); Ibrahimovic 9. Not used: Romero, Rojo, Carrick, Rashford.