The Jets reached 70 points for the season, moving them one in front of Washington and into the eighth spot in the Eastern Conference playoff race.
The seven goals represented the second-largest output in a game for the Jets this season and brought them their first win in three outings.
Kane scored twice and had two assists. He opened the scoring 4:01 into the contest and Jim Slater's wrist shot 2 minutes later gave Winnipeg a 2-0 lead after one period.
Pavelec made 33 saves in the 10th shutout of his five-year career.
Jose Theodore was removed from the game in the third period after giving up four goals on 24 shots. Clemmensen let in three goals on eight shots.