Pavelec won for the first time since Nov. 19, helping the Jets snap a two-game skid and pick up their 10th victory of the season.
The New York Islanders, Carolina Hurricanes, Columbus Blue Jackets and Anaheim Ducks are the only teams in the NHL not to have won 10 games.
The shutout was the eighth in Pavelec's five-year career.
Bryan Little produced the only goal, putting a backhander past Mike Smith 6:53 into the first period.
Phoenix had won two straight. Smith stopped 30 shots.
Notable deaths of 2014 [PHOTOS]