Higuain's marker came on a 25-yard strike that went in off the right post.
Josh Williams and Dominic Oduro followed with scores to salt the win away for the Crew (1-0-0).
Chivas (0-1-0) fell in its first game under new Coach Jose Luis Sanchez Sola.
Ray Liotta sues skin care company over use of likeness
Boston schools pull out free condoms over wrapping complaints