Angel Di Maria gave Real the lead on 15 minutes and substitute Benzema doubled their advantage shortly after being introduced at the interval.
Jose Villarreal halved the Galaxy's deficit with a spectacular strike on the hour mark but Benzema restored Madrid's two-goal advantage with a 74th-minute header.
"In general it was a good performance from the team," said Madrid coach Carlo Ancelotti. "We played well. We had a good combination in the front. We had a lot of opportunities."
The visitors controlled proceedings from the start, Cristiano Ronaldo hitting the crossbar with a header on six minutes and Galaxy goalkeeper Brian Rowe saving a Denis Cheryshev shot.
The Spanish giants took the lead when Isco launched a ball from deep in his own half and found Ronaldo, who eluded three defenders and put it on a plate for Di Maria.
Ronaldo departed in the flurry of half-time substitutions that brought on Benzema, who took just six minutes to find the net when he fired home from Isco's looping pass.
Villarreal pulled a goal back on 63 minutes, taking two touches to make space before rifling a superb strike past Diego Lopez.
But Benzema had the final say, heading home Di Maria's cross to seal a comfortable victory.