109,318 fans packed into Michigan Stadium, beating the previous record of 101,799, which was set at the 1984 Olympic final when France beat Brazil 2-0 at the Rose Bowl in Pasadena, California.
That venue and tournament saw the only other six-figure football attendance in U.S. history, as 100,374 saw Yugoslavia defeat Italy 2-1 for the bronze medal.
Saturday's figure also eclipses the attendance for the World Cup final in 1994, which saw 94,194 watch Brazil take on Italy in the most high-profile game to take place in America to date.
Javier 'Chicharito' Hernandez grabbed a goal for the Red Devils after Ashley Young scored two either side of Gareth Bale's penalty, continuing Louis van Gaal's positive start as United boss.
United now move on to face Liverpool in the final of the International Champions Cup on August 5 at Sun Life Stadium in Miami, while Madrid will prepare for the Uefa Super Cup against Sevilla in Cardiff.