Dominic Oduro gave the Crew all the scoring they would need in the 15th minute off a pass from Jairo Arrieta and Josh Williams doubled the advantage 11 minutes later after being set up by Higuain.
Higuain added his penalty shot goal in the 47th for Columbus (3-2-3).
D.C. dropped to 1-6-1 with its fifth straight loss.
The start of the game was delayed nearly an hour when a fire broke out inside the scoreboard at Columbus Crew Stadium.
No one was injured as fans were moved out of the section of the stands nearest the scoreboard.
The fire began in its speaker cabinet and no public address system was available during the contest.