Shortly after, Higuain almost made it two but his free kick curled narrowly wide of Bendik's far post as Columbus looked in control.
Both sides missed good chances through Sebastian Giovinco and Kamara respectively, before the Crew did succeed in doubling their advantage on 36 minutes.
Tony Tchani picked up a square ball from Ethan Finlay, before trying his luck from outside the area and beating Bendik from the edge of the box.
Prior to that, Marco Delgado spurned arguably the best chance of the half by heading wide of Steve Clark's net from less than six yards out.
On 48 minutes, the hosts took a big step toward the victory when Finlay added a third, but Giovinco struck an immediate riposte with a first-time volley within a minute of the restart to restore the two-goal deficit.
Jozy Altidore completed the comeback one minute from time when he was brought down in the penalty area and a spot kick was awarded. The former Sunderland man took the penalty himself and fired the effort past Clark to rescue a point for his side.