It was Pavelec's first shutout of the year and the seventh of his career.
Rick DiPietro made 23 saves for the Islanders, who lost their sixth straight game.
Winnipeg struck first when Kane received a pass at center ice and weaved past a defender at the offensive blue line. His initial shot attempt at the left circle was blocked by an Islanders defender, he then gathered the puck and fanned on a second shot attempt before sending a backhander past DiPietro just 4:21 into the game.
Kane was then issued a penalty shot near the mid point of the period when he was hooked by Islanders defenseman Travis Hamonic on a breakaway, but he failed to convert on the chance as his shot fired off the right post.
The Jets held the Islanders scoreless through the second period despite having three penalties called against them, then extended their lead late in the third when Oduya attempted a cross-ice pass from the left circle that deflected off the stick of the Islanders' Andrew MacDonald and into the net with 3:56 left in the game.
Burmistrov shot the puck into the vacated net 1:40 later to seal the win for Winnipeg.
Jets defenseman Tobias Enstrom missed the game due to an upper body injury...The Islanders last win was a 4-2 decision over the Rangers on October 15...New York fell to 3-3-1 at home this season...The Jets improved to 3-1-0 on a seven-game road trip.