Price turned aside all 34 shots he faced.
The win, coupled with the Boston Bruins' loss to Philadelphia earlier Saturday, gave the Habs a three-point advantage atop the division standings.
P.K. Subban supplied an assist on all three Montreal scores.
The Rangers, struggling to secure the eighth and final Eastern Conference playoff spot, got 23 saves from Martin Biron in their seventh in 10 contests.
Celebrity Families of 2014 [PHOTOS]