Henrik Lundqvist made 19 saves in his third shutout this season and fifth in two seasons. His best stop came in the first period when he turned aside Michael Ryder on a breakaway out of the penalty box.
Hossa found the net twice in the second period, giving the emerging left winger eight goals in 11 games. Playing on a line with captain Jaromir Jagr and Michael Nylander, in the absence of injured forwards Martin Straka and Brendan Shanahan, Hossa matched his career high of 10 goals set last season.
Jagr scored his second power-play goal in two games to give the Rangers a much-needed win. New York began the night tied for 11th in the Eastern Conference, seven points and three places below the playoff cutoff.
Matt Cullen’s empty-net goal, with an assist from Hossa, sealed it with just under a minute left.
The Rangers moved within six points of the Canadiens, who entered Tuesday with a hold on seventh in the tight race for the playoffs. Montreal had won four of five.