Toronto (22-13-4) remained fifth in the Eastern Conference standings, moving four points ahead of idle Ottawa with its fifth win in six games.
Derek Stepan pulled New York into a 3-3 tie at 9:00 of the third period, but Kessel put Toronto back ahead 39 seconds later.
The Rangers (19-16-4) remain tied with the idle New York Islanders for seventh in the Eastern Conference with 42 points.
BRUINS 6, HURRICANES 2
In Boston, Brad Marchand scored two goals and Tuukka Rask stopped 40 shots, leading the Bruins over struggling Carolina.
Rich Peverley, Andrew Ference, Jordan Caron and Nathan Horton each added a goal, and defenseman Dennis Seidenberg established a career-high with three assists for Boston, which moved a point behind Montreal in the Northeast Division.
The Bruins won for the fourth time in five games by scoring a season-high in goals.
Patrick Dwyer and Drayson Bowman scored for the Hurricanes, who lost for the 12th time in 13 games, 11 of them coming in regulation.
Carolina has allowed four or more goals in 10 of its last 14.