Anthony Martial secured victory with two goals early in the second half after former United player Anthony Fletcher had cancelled out Zlatan Ibrahimovic’s early opener.
Ibrahimovic added gloss to the scoreline with his second of the night in injury time.
United manager Mourinho was not seen inside the arena after accepting a touchline ban earlier in the day for his sending-off during Sunday’s Premier League clash between the same two sides.
From wherever the Portuguese chose to watch, he will presumably have been pleased with his side’s high-energy and clinical performance.
“A secret,” said Mourinho, when asked where he watched the game. “I was in contact with the bench and to be honest yesterday we worked really well in a way that everybody was prepared so at half-time I could be face to face with the keepers and on top of that I trust my people, I trust my assistants with the information but I am really happy with the players,” said Mourinho, who paid tribute to Brazilian side Chapecoense after the air tragedy in Colombia.
The only disappointment for United fans was the failure of captain Wayne Rooney to score the goal that would have equalled Bobby Charlton’s club record on his return to the starting line-up.
That will now have to wait a little longer as a booking for dissent means Rooney will be suspended for this weekend’s trip to Everton.
The supporters did at least get to welcome Bastian Schweinsteiger back to the pitch after his long exile with a late substitute cameo.
United conceded after just 90 seconds against West Ham on Sunday but roles were reversed this time as the hosts made a blistering start and swept into a second-minute lead.
Rooney found Henrikh Mkhitaryan in space with a good touch and the rejuvenated Armenian presented Ibrahimovic with an inviting opportunity with a neat backheel.
The Swede showed great composure as he calmly dinked the ball over the advancing Adrian for his 10th United goal.
Ibrahimovic took a blow for his troubles as Adrian caught him with his studs in his follow-through and the goalkeeper might have been lucky to escape punishment.
Ibrahimovic had another shot blocked by Winston Reid and two rapid United counter-attacks ended with Martial first being felled just outside the area and then blasting over. Rooney forced Adrian to palm wide from a curling free-kick.
The Hammers offered little until equalising against the run of play 10 minutes before the interval. David de Gea was at fault as he failed to hold a long-range Dimitri Payet strike and United academy product Fletcher snaffled his chance. The 21-year-old, who left the Red Devils in the summer, did not overdo his celebrations but punched the air in delight.
United picked their game up again after the break, reclaiming their lead after 48 minutes as Mkhitaryan squared for Martial to sweep home his first.
The Frenchman added another to make the game safe just after the hour, this time with a simple finish at the end of a slick move involving Ibrahimovic and Antonio Valencia.
Rooney had been influential throughout but at this point he noticeably moved up a gear as he chased his landmark goal.
He showed some of his aggression as he won possession and curled a shot wide. He suffered a cut cheek after being kicked in the face by Reid in another attack but that only seemed to fire him up more.
It was not to be for him on this occasion, however, with Ibrahimovic tapping home the fourth late on.
de Gea, Valencia, Jones, Rojo, Shaw (Blind 46), Ander Herrera, Carrick, Mkhitaryan (Rashford 90), Rooney, Martial (Schweinsteiger 87), Ibrahimovic.
Mata, Lingard, Romero, Schneiderlin.
Adrian, Kouyate, Reid, Ogbonna, Antonio (Lanzini 58), Obiang, Fernandes, Cresswell (Masuaku 45), Feghouli, Fletcher, Payet (Zaza 76).
Randolph, Nordtveit, Noble, Collins.
Mike Jones (Cheshire).