Real Madrid led 2-0 early in the second period courtesy of goals from Casemiro and Isco, and the Spanish champions held on to land the title despite Romelu Lukaku's first Man United goal making it an uncomfortable conclusion for Los Blancos.
Gareth Bale was named in the Real Madrid XI despite his recent injury problems and the speculation surrounding his future, while Cristiano Ronaldo, having not represented Los Blancos during pre-season, was included among the substitutes.
As for Man United, there were competitive debuts for Victor Lindelof, Nemanja Matic and Lukaku, while Jesse Lingard was preferred to the likes of Marcus Rashford and Anthony Martial in the final third of the field.
Real Madrid came close to opening the scoring inside three minutes when the spin on a high ball saw Bale get the better of Mkhitaryan inside the Man United box, but the Welshman's instinctive effort just missed the crossbar.
Lukaku, Pogba and Mkhitaryan were all heavily involved for Man United in the opening 10 minutes, and the latter might have won a free kick just outside the Real Madrid box after placing the ball through the legs of Sergio Ramos, but replays showed that the Armenian went down under little pressure.
Madrid had another opportunity in the 16th minute when Casemiro wriggled free of Matteo Darmian to meet a Toni Kroos corner inside the United box, but the Brazilian's bullet header rattled off the crossbar.
Isco was next to come close for the Champions League holders after releasing one from the edge of the United box, but the Spaniard's effort missed the crossbar, before David de Gea had to keep out a fizzed cross from Luka Modric as the pressure increased.
Real Madrid finally made the breakthrough in the 24th minute when Casemiro placed an inch-perfect Carvajal pass into the bottom corner, although replays showed that the midfielder had been in an offside position.
The Spanish champions continued to dominate in the period that followed, but the water break on 30 minutes allowed Man United boss Jose Mourinho a chance to rally his troops as the Red Devils looked to stay in the Super Cup ahead of the second period.
Real Madrid had a decent chance to double their advantage in the 42nd minute when Karim Benzema found space inside the United box, but the Frenchman's low strike was saved by De Gea, before Navas kept out a header from Lukaku down the other end of the field.
Rashford came off the bench at the interval, replacing the ineffective Lingard in the process, but it was Real Madrid that continued to look the more likely to score the game's second goal.
Only a wonderful De Gea save prevented Kroos from finding the corner with a powerful effort in the 48th minute, before a smart challenge from Chris Smalling saw Marcelo's goal-bound strike blocked wide of the post.
Real Madrid were absolutely dominant, however, and Zinedine Zidane's side doubled their lead in the 52nd minute when Isco played a one-two with Bale before sliding the ball into the bottom corner of the net.
Man United should have been back in the match less than two minutes later when Navas palmed a close-range Pogba header into the path of Lukaku, but the big-money arrival from Everton somehow missed the crossbar.
Marouane Fellaini was the second player off the Man United bench as Mourinho looked to provide Real Madrid with a different threat, but the Spanish champions continued to dominate, and only the crossbar prevented Bale from sending his team 3-0 ahead just past the hour mark.
Man United were back in the match in the 62nd minute, however, when Lukaku smashed the ball home from close range after Real Madrid goalkeeper Navas had palmed a Matic strike straight to the Belgian international.
Man United had a wonderful chance to level the scores in the 82nd minute when Mkhitaryan fed Rashford inside the Real Madrid box, but the England international could not find a route past Navas.
Ronaldo then came off the bench to a rousing reception in the 83rd minute, but it was the English giants that were on the front foot, and Rashford missed the crossbar with a free kick from an advanced position five minutes from time.
Mourinho's side continued to look for a leveller in the seven minutes of additional time, but it was Real Madrid that came the closest - De Gea keeping out a close-range effort from Asensio as Los Blancos landed more European silverware.
Man United will now switch their attention to domestic matters as the Red Devils prepare to open their 2017-18 Premier League season at home to West Ham United on Sunday afternoon. Next up for Real Madrid, meanwhile, is the first leg of the Spanish Super Cup against Barcelona at Camp Nou on the same day.