Trailing 1-0, the Crew notched the equalizer after Columbus rookie defender Chad Barson was knocked down in the box by Houston's Andrew Driver.
Higuain followed by converting his fourth goal of the season for Columbus (4-4-5).
Warren Creavalle tallied in the first half for the Dynamo (6-4-4), who remained winless in four games.
Megyn Kelly: Santa Claus and Jesus are both white men
Video of Victoria’s Secret models trying to 'twerk' hits Instagram