United took the lead when Nick DeLeon robbed Higuain of the ball in midfield and slipped a through-ball down the left for Fabian Espindola, who drilled an effort past Steve Clark into the roof of the net.
Jimenez almost got his side level just before the break when he fired a shot from outside the area, but his effort went just past the post.
After the break, DC had the chance to double their lead on a counter-attack as DeLeon broke upfield and threaded Espindola through on goal, but the striker couldn't control the ball and the Crew defence cleared the danger.
The home side pressed again and Josh Williams got in down the right and cut the ball back to Jimenez, who spurned another chance as he latched onto the cross, firing wide of the target.
Columbus were reduced to 10 men when Bernardo Anor was given a straight red card for a two-footed challenge on Perry Kitchen.
However, the Crew managed to rally to get their equaliser as Jimenez finally found the back of the net when he collected a long ball down the left and curled a shot past Dykstra from the edge of the area.