Brazilian midfielder Casemiro struck the opener with a left-foot strike midway through the first half while Spain midfielder Isco consolidated Real's advantage with a slick finish in the 52nd minute at the National Arena in Skopje, Macedonia.
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.
"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."
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.
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.
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)