Zardes scored in the 27th, Higuain in 53rd and Hector Jimenez in the 66th to stake the Crew (5-6-1, 16 points) to a 3-0 lead, before Daniel Steres scored from a Sebastian Lletget free kick in the 87th to avoid the shutout.
The Galaxy (7-3-1, 22 points) have lost two straight and missed an opportunity with a win to move a point ahead of the Western Conference and MLS-leading Los Angeles FC.
Zardes, the former Galaxy forward who had 19 goals for the Crew last season, made it 1-0 with his fourth goal of the year, but his first in seven games.
Robinho served a ball to the top of the goal box, where a tightly marked Zardes extended his left foot for the redirect and Crew's first lead in 526 minutes. Higuain got the secondary assist, the 62nd assist of his career to surpass Robert Warzycha for the career Crew lead.
That proved crucial, because Higuain doubled the lead three minutes later. He ran onto a layoff by Zardes 40 yards out and dribbled to the penalty area before putting a low shot to the right corner, past the outstretched arms of David Bingham for his first goal of the season and 55th in MLS.
Jimenez, another ex-Galaxy player, added a third goal in the 66th minute, cleaning up a loose ball after Zardes was tackled in the box. It was his first goal since April 2014.
The Crew entered the match having scored nine goals this season.
Columbus stays home to play Los Angeles FC on Saturday, the same day the Galaxy host New York City FC.