Madrid dominated from the start and led when Casemiro – who earlier hit the bar – slid in a half volley.
They doubled their lead when Isco calmly slotted in from eight yards after a neat one-two with Gareth Bale, who started ahead of Cristiano Ronaldo.
New £75m striker Romelu Lukaku tapped in before Marcus Rashford scuffed wide.
The Europa League winners were given encouragement by Lukaku’s strike, despite rarely threatening the Madrid goal in the previous hour, and could have scored a barely deserved equaliser through half-time substitute Rashford with nine minutes left.
United were unable to create another clear-cut chance as Madrid became the first team to retain the Super Cup since 1990.
With temperatures over 30C in the Macedonian capital, the match was twice stopped for scheduled cooling breaks implemented by governing body Uefa.
The Red Devils have spent £146m this summer on Everton striker Lukaku (£75m), Chelsea midfielder Nemanja Matic (£40m) and Benfica defender Victor Lindelof (£31m) as they look to improve on a disappointing sixth-placed finish in the Premier League last season.
All three new signings started as Mourinho named a strong side against the European champions.
Only Ronaldo was missing from the Madrid team which started their victory against Juventus in the Champions League final, providing a stern test for Mourinho’s new-look side.
But United struggled against the continent’s best, particularly in the first half, as Madrid controlled the tempo with their crisp and purposeful passing.
The English side were unable to effectively keep possession before half-time – managing just 39% of the ball – and mustered only one shot on target when Lukaku headed straight at Madrid keeper Keylor Navas.
Mourinho introduced teenager Rashford at the break, looking to stretch the Spanish club – who the Portuguese boss managed between 2010 and 2013 – on the break.
Although the Red Devils did improve in the second half, they still looked well short of being able to compete with Europe’s most talented sides going into their return to the Champions League this season.
Madrid continued to create chances throughout. Bale smashed against the bar when the score was 2-0, while David de Gea also produced superb saves to stop Toni Kroos, Karim Benzema and Marco Asensio.
The former Southampton player had a chance to prove his worth to Zinedine Zidane as he started up front alongside Karim Benzema.
He instinctively fired over early on, then set up Isco with a perfectly weighted pass before smashing a rising right-footed drive against the bar.
Bale, who was brought off after 75 minutes, will be pleased with his contribution in an impressive team performance.
However, if Madrid do sign exciting Monaco teenager Kylian Mbappe then it would appear Bale could become a peripheral figure at the Bernabeu.
After the game, Bale said he has not been told he can leave.
“I’m just concentrating on football and not listening to anything,” he said. “I’m enjoying myself playing here.”
Competitive top-level European club games rarely include drink breaks, but they were implemented by Uefa in Skopje after temperatures remained over 30C during the match.
A heatwave nicknamed ‘Lucifer’ has hit southern Europe with temperatures in the Macedonian capital regularly rising above 40C this week.
The match paused twice – once at the 30-minute mark and again after 72 minutes – for both sets of players to rehydrate.
Both managers used the pair of two-minute breaks to gather their players around and issue some tactical instructions.
Bale said he felt his team coped well with the heat, adding: “It helped we have been training in 38C heat in Madrid.”
Jose Mourinho says:
“I think we did well. We lost 2-1 which, I think, shows the result was really short, and one of the goals was offside so with a good VAR it would be 1-1 and extra time.
“I think they could score more goals than they did, we could score more goals than we did. They had a period of dominance in the middle of the first half, we had a period of dominance in the middle of the second half and some balance in the beginning of the game.
“We were playing against a team of fantastic players and we discussed the result until almost the end, not the end but almost the end.”