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.
Scarlett Johansson steps out with fiance after pregnancy reveal
Susan Sarandon 'very excited' about daughter's pregnancy