Luis Argudo drew the foul against Ken Krolicki that set up Zardes, who put in the go-ahead goal just under the crossbar for the Crew (2-0-0).
Ignacio Piatti cut the deficit to 2-1 in the 59th minute.
Federico Higuain opened the scoring for Columbus on a penalty in the 12th minute with goalkeeper Evan Bush guessing the wrong way. It was Higuain's 50th career regular-season MLS goal.
Zardes made it 2-0 in the 15th minute with a close-range putback off a free kick that clanked off the crossbar.