Kane also added an assist and rookie Anthony Peluso registered his first career NHL points with two assists as the Jets closed out a five-game road swing with a 4-1-0 mark.
Ondrej Pavelec turned aside 30 shots to earn the victory.
The Rangers, meanwhile, continued to struggle, falling for the fourth straight game.
Ranges goalie Henrik Lundqvist made 28 stops.
Wisconsin business offering 'therapeutic cuddling' forced to close
N.J. man wakes up from 10-hour sleep with knife in back