It means the 21-year-old will miss three games after the worldwide break and comes at a time when he is struggling to break into United's line-up.
It was a rewarding first period for Mourinho and his team, not to mention the 2,400 visiting supporters at Turf Moor who showed their backing for Mourinho.
A banner is flown over the stadium prior to the match between Burnley FC and Manchester United
United could ill afford the pressure to ratchet up any higher heading into the worldwide break after chastening back-to-back defeats against Brighton and Tottenham. If the United boss' celebrations are to continue, Lukaku will have a big role to play. Shaw's confidence will just grow from now on and Mourinho must use that the best way he can.
The team now go into the global break after an impressive victory against last year's surprise package of the Premier League.
In contrast, there was a demonstration by fans against the club's executive vice-chairman Ed Woodward with a plane flown over the Lancashire ground towing a banner that read: "Ed Woodward, a specialist in failure".
United started the season with two defeats from their first three games, but Mourinho drew the focus onto himself, rather than performances on the pitch, with a number of eye-catching public statements, including quoting German philosopher Georg Hegel and asking for more "respect" for his achievements.
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He is the first Austrian in the last-eight at the US Open since Thomas Muster in 1996. "I just said "I am very sorry". The 32-year-old has certainly been pushed in his last two matches, both of which have gone to four sets.
"No, no", the United midfielder said.
"We should have scored before we scored the goals and we should have scored the penalty that would kill the game and also the best chances after the penalty".
Sunday's victory provided welcome relief to Mourinho, his players and his staff before the global break, where United would have not had the chance to alter the narrative surrounding the club for a fortnight. This is one of the greatest clubs ever.
Two first half Romelu Lukaku goals handed United the points, with Paul Pogba having a penalty saved by Joe Hart after the break, before Marcus Rashford was sent off after thrusting his head into former Red Phil Bardsley's.
Allegri: Ronaldo needs time to adjust to Serie A
Both Ronaldo and Manchester United are struggling at their respective ends. If I say it again now it is not because of two defeats. The Fiver: sign up and get our daily football email.
Mourinho was in the stands at Old Trafford to see Dalot's assured performance in a 1-0 win over Stoke City.
The Spaniard, 30, has never really been a Jose Mourinho favourite even from their days at Chelsea, but he has at least managed to make it to nearly five years as a United player following a January 2014 move.
China hosts African leaders as foreign aid criticism intensifies
China's growing clout in Africa is also drawing criticism that more African countries are getting caught in a Chinese debt trap. This is the third such summit; the first was in Beijing in 2006 and the second was held in South Africa three years ago.