United's new striker Romelu Lukaku got his first competitive goal for the club to reduce the deficit just past the hour with a simple finish on the rebound in the annual showdown between the European champions and Europa League holders.
That sparked a brief period of pressure from Jose Mourinho's United side and they could have drawn level when Marcus Rashford burst through but he was denied by Keylor Navas' save, ensuring Real won their fifth international trophy under Zinedine Zidane.
"We were superior for almost all of the game and it's important that we've started the season by winning a trophy against a team that did everything they could to win," said Real captain Sergio Ramos.
"Towards the end they had more chances and tried direct play with physical players but we stayed calm in the tense moments and kept the ball. Aside from the final minutes, we had a great game."
Mourinho added: "We were playing a team full of fantastic players but we discussed (contested) the result until almost the end. We gave them a fight but have reasons to leave optimistic and proud."
MORE QUALITY
The United coach's admission before the game that Real had much more quality than his side was confirmed as the Champions League winners monopolised possession and nearly took an early lead when Gareth Bale sent an instinctive shot narrowly over the bar.
Defensive midfielder Casemiro then crashed a diving header against the bar before meeting Dani Carvajal's perfectly weighted cross on the half-volley to add to his goal in the Champions League final win over Juventus.
Europa League holders United barely mustered an effort at Navas in the first period, the club's record signing Paul Pogba wasting their only chance with a shot that was easily blocked when Henrik Mkhitaryan was unmarked screaming for the ball.
Real continued to dominate after the break as United struggled to press their opponents in the heat and humidity that was so intense the teams took a water break in each half.
A fine save by United keeper David de Gea prevented Toni Kroos from scoring moments after the restart while their defender Chris Smalling did well to block a goal-bound effort from Marcelo and send it into the side netting.
Madrid did not relent, however, and standout performer Isco deservedly doubled their advantage with an arrowed finish beyond his Spain team mate De Gea after bursting into the area and exchanging a pass with Welshman Bale, who later rattled the bar.
Real's dominance waned towards the end as United forced their way back into the game but there was little question the all-conquering Spanish giants were worthy winners when Ramos hoisted the trophy into the Skopje air.
($1 = 0.7700 pounds)
(Reporting by Richard Martin; Editing by Ken Ferris)
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