The hosts opened the scoring when Jack Roslovic's wrist shot from the faceoff dot made its way past Montembeault at 8:36 of the first.
The Habs headed to the room trailing 1-0 after the first period, with the Jackets leading 9-4 in shots in the opening frame.
Columbus doubled its lead late in the second, when Patrick Laine's pass hit Roslovic's leg and went in with 4:08 to go in the period.
Then, Laine made it a 3-0 game just 90 seconds later while Mike Hoffman was in the box for slashing.
The Habs finally got on the board 47 seconds later while on a power play of their own, with Ryan Poehling redirecting Nick Suzuki's wrister from near the blue line to reduce Columbus' lead to two with his sixth of the season.
Suzuki and Hoffman got the assists.