Brassard scored his first of the season with only 12.9 seconds showing on the OT clock.
Benoit Pouliot had a goal and an assist and Mats Zuccarello also scored for New York, which rallied from 1-0 and 2-1 deficits in the final game of its season-opening, nine-game road trip. Cam Talbot stopped 32 shots while filling in for injured regular Henrik Lundqvist.
The Rangers (3-6), who went to overtime for the first time this season, will host Montreal in the opener at renovated Madison Square Garden on Monday.
Introducing the new official NHL App, available for iPhone, iPad and Android smartphones and tablets. A host of new features and improved functionality are available across all platforms, including a redesigned league-wide scoreboard, expanded news coverage, searchable video highlights, individual team experiences* and more. The new NHL App on your tablet also introduces new offerings such as 60fps video, Multitasking** and Picture-in-Picture.
*Available only for smartphones
** Available only for suported iPads