Mattias Ekholm gave the Preds the lead but second-period goals from Brendan Gallagher and David Desharnais turned the game on its head before Ryan Ellis levelled things and Filip Forsberg grabbed an overtime winner.
The Tampa Bay Lightning are just one point behind the Habs in the Atlantic Division after a 4-3 win over the Florida Panthers.
Brenden Morrow and Tyler Johnson had the Bolts two up but Jussi Jokinen, Brandon Pirri and Jonathan Huberdeau put the Panthers ahead going into the third period.
Nikita Kucherov grabbed an equaliser 90 seconds into the final stanza and Ryan Callahan snatched the win.
The Minnesota Wild tightened their grip on a play-off spot in the Western Conference with a 2-1 shootout win over the New York Islanders.
John Tavares and Zach Parise exchanged goals in regulation with Parise scoring the vital penalty shot after a scoreless overtime.
The Columbus Blue jackets caused an upset as Scott Hartnell’s hat-trick led them to a 5-3 win over the Pacific Division-leading Anaheim Ducks.
Ryan Johansen and Nick Foligno also scored for Columbus with Ryan Kesler, Andrew Cogliano and Matt Beleskey responding.
Alexander Steen grabbed the vital goal as Central Division leaders the St Louis Blues beat the Pittsburgh Penguins 3-2 while the Arizona Coyotes also needed the extra period to beat the Detroit Red Wings 5-4, Mark Arcobello with the winner.
The Los Angeles Kings beat the New York Rangers 4-2 to move within two points of the Winnipeg Jets in the race for the final wild card spot in the west.
The Jets went down 5-2 to the Vancouver Canucks in the final game of the night to end a five-game winning streak.