The home side took the lead in the second minute when Will Trapp picked out the run of Finlay with an inch-perfect pass and the forward fired the ball into the top corner of the net from a tight angle.
Aaron Schoenfeld slipped behind the Impact defence minutes later and fired a shot across the face of goal which went just past the post.
An error from Matteo Ferrari almost ended in disaster for Montreal as Schoenfeld released the run of Higuain, but his chipped effort went just the wrong side of the post.
In the second half, the Crew were handed the chance to double their lead when they were awarded a penalty. Higuain took the spot kick and fired his effort past the outstretched hand of Bush.
Columbus somehow didn't secure the three points in the 86th minute when Tony Tchani raided forward and fired a shot at goal only to see his effort hit the woodwork.
The ball fell kindly to Bernardo Anor two yards from the empty net, but he incredibly struck the post as well, although his side were able to see out victory at Columbus Crew Stadium.