In front of a crowd of 109,318 at Michigan Stadium - a record attendance for a game of football in the United States - Ashley Young netted twice in the first half either side of Gareth Bale's penalty.
Real posed more of a threat in the second half, but substitute Javier Hernandez added a late third to ensure Louis van Gaal's side topped Group A.
Inter's 2-0 win over Roma earlier in the day had momentarily sent Walter Mazzarri's men to the summit of the group, and United knew they needed to avoid defeat in 90 minutes against Real to usurp the Italian side and book their place against Liverpool in Monday's final.
United looked sharper for much of the encounter, although there was an injury concern as Danny Welbeck was forced off shortly before the break.
Real, unable to qualify before play began, introduced Cristiano Ronaldo off the bench for the final 15 minutes, but the Portugal star was unable to make much of an impression against his former club.
United started the better of the two sides without carving out any clear goalscoring opportunities, Darren Fletcher's 20-yard drive wide of the post representing their best effort in the opening 15 minutes.
After Fletcher exchanged passes with Wayne Rooney, the ball was worked on to Welbeck, who teed up Young to place a finish inside Iker Casillas' near post.
Two minutes later, United were back in front as Young's teasing cross from the left crept in at the far post with Rooney failing to make any connection with his head.
The Welshman continued to pose a threat and struck the outside of the right-hand post with a dipping free-kick in the 55th minute.
Hernandez went agonisingly close seven minutes later, failing to get sufficient contact on Jesse Lingard's inviting cross from the right.
The Mexican made no mistake 10 minutes from time, however, diving in at the far post to head Kagawa's perfectly weighted cross into the net and round off an impressive performance from United.
