Angel Di Maria latched onto a Cristiano Ronaldo lay-off to dink home the opener after 15 minutes of play at the University of Phoenix Stadium.
Benzema, who was one of a number of players introduced at half-time as Ronaldo departed, made it two on 51 minutes with a neat finish.
Nineteen-year-old Jose Villarreal ensured he would never forget the encounter with a stunning effort 12 minutes later to make things interesting, but France international Benzema swooped with his second with 16 minutes left on the clock to snuff out any hope the MLS side harboured of getting back into the game.
Real and the Galaxy are two of eight teams participating in the International Champions Cup, played across the United States.
Juventus, Internazionale, AC Milan, Chelsea, Everton and Valencia make up the rest of the draw.
- Sports & Recreation
- Cristiano Ronaldo
- Angel Di Maria