Casemiro, who scored from the spot in the second half to cancel out Jesse Lingard’s opener, missed the crucial penalty after De Gea kept out efforts from Mateo Kovacic and Oscar Rodriguez.
Only three of the 10 spot-kicks taken in the shootout were successful, with Daley Blind and Henrikh Mkhitaryan the scorers for Jose Mourinho’s side.
Anthony Martial created Jesse Lingard’s first-half opener for United with a brilliant piece of skill on the left.
Martial wove past Luka Modric and Dani Carvajal, then roll a pass to Lingard for United’s opener as Raphael Varane closed in, it was easy to see why Mourinho’s predecessor, Louis van Gaal, sanctioned his £36m transfer two years ago.
Casemiro levelled for Real from the penalty spot after United’s new £31m defender Victor Lindelof brought down Theo Hernandez with a rash challenge.
It was not a great night for Lindelof, who compounded his error during the game with a miss from the spot.
Another negative for United was Ander Herrera lasting only six minutes before going off with a hip injury.
Manchester United have now won all four of their matches in the United States and meet Barcelona in their final tour game in Washington on Wednesday.
Wales forward Gareth Bale started for Real in their first pre-season game.
Real play Manchester City in Los Angeles on Wednesday before meeting Barcelona in Miami on Saturday.
Martial set the tone by blazing the first kick way over. After two penalties each, the score was 0-0.
Real were even worse. Only Quezada scored for them, meaning United won when Casemiro blasted against the bar after Daley Blind’s unconvincing effort had given the Premier League side the advantage.
Manchester United boss Jose Mourinho:”It was a good training session. A very good first half against a top Real side. In the second half we lost motivation, intensity and appetite to play against their youngsters. My players in the second half were disappointed not to play against their best players.
“We have one injury to Ander Herrera, I don’t know how he is but it has to be painful to come off so soon.
“Three out of 10 penalties – that’s pre-season. I didn’t choose my best penalty takers.”