The Jets, battling for the lead of Southeast Division, forced extra time when Bryan Little notched an equalizer with 2:01 left in regulation.
Frans Nielsen and and John Bailey each provided a goal and an assist for New York. Evgeni Nabokov turned aside 24-of-28 shots for the Islanders, who improved to 8-0-2 in their last 10 games and moved four points ahead of ninth-seeded Winnipeg in the Eastern Conference standings.
Matt Martin and Michael Grabner also scored for the Islanders.
Kyle Wellwood scored twice and Pavelec finished with 29 stops for Winnipeg, which entered the contest two points behind division-leading Washington.