Chris Kreider and Braden Schneider also scored for the Rangers (22-12-6), who have won three in a row.
Jaroslav Halak had 17 saves in the win.
After a scoreless opening period that saw a total of 10 shots between the two sides, Kreider broke the ice 7:43 into the second.
Montreal’s bottom-ranked power play continued to struggle when an errant pass from Juraj Slafkovsky was intercepted by Kreider who made no mistake converting the breakaway.
Schneider then doubled the Rangers's lead at 12:28 with a point shot into the top corner of the net.
New York did not stop there, padding its lead behind Chytil's 10th of the season just 59 seconds later.
Montreal came out firing in the third period, creating a handful of strong chances early but to no avail.
The Canadiens finally put an end to Halak’s shutout bid, when Armia hopped on a bouncing puck in the slot with 5:14 remaining in the contest.
Chytil added an empty netter with 1:10 left to seal the victory.
GALLAGHER STILL OUT
A Canadiens team desperately lacking veteran leadership will have to do without one of their most senior players. Brendan Gallagher was listed as out with a lower-body injury. The winger has now missed 14 of the club’s 39 games.
SPECIAL TEAMS WOES
Montreal's 32nd-ranked power play failed to convert on their lone man advantage but conceded their first short-handed goal of the year. The Canadiens have failed to score in nine of their last ten power plays.
Canadiens: Host the St. Louis Blues on Saturday.
Rangers: Face the Devils in New Jersey on Saturday.
This report by The Canadian Press was first published Jan. 5, 2023.
Elias Grigoriadis, The Canadian Press