Yanic Perreault and Ed Jovanovski each scored to lead the Coyotes to their season-best fourth straight win.
It was the 49th shutout and the 438th victory of Joseph's 17-year career. He surpassed Hall of Famer Jacques Plante for sole possession of fifth place on the NHL's career wins list, and followed his 8-0 victory over San Jose last week with another perfect performance.
Next up for CuJo: Terry Sawchuk, who's fourth with 447 wins.
Cam Ward stopped 26 shots for the Hurricanes, who were shut out for the second consecutive game and sixth time this season, at times drawing boos from the RBC Center crowd when they couldn't manage a shot on goal during a third-period power play.