After failing to win any of their last four and coming into the clash on the back of a 3-0 mauling by Philadelphia Union, Columbus started as though they had a point to prove.
Just before the break, Waylon Francis looked like snatching Crew a half-time lead, but Bush produced the goods once more to ensure his side parity at the interval.
The hosts were made pay for their first-half profligacy as Maxim Tissot then fired Montreal into the lead within 10 minutes of the restart.
Montreal doubled their lead in the 78th minute when they hit the home side on the counter-attack when Piatti fed the run of Andres Romero, who slotted the ball past Clark.
Crew pushed to get back into the game and were given hope as Federico Higuain found the net when he teed himself up inside the box and drilled a low strike into the bottom corner.
Columbus made a late surge to earn a point, but the visitors held out to secure the victory to leave themselves in ninth place in the Eastern Conference, while the Crew remain in sixth place.