Olli Jokinen, Blake Wheeler, Devin Setoguchi and Michael Frolik also scored as Winnipeg snapped a five-game losing streak and handed Maurice a resounding victory in his first game behind the Jets' bench.
He took over after Claude Noel was fired Sunday amid the team's season-worst skid. It was Maurice's first NHL game since being fired by Carolina in November 2011.
Ondrej Pavelec earned the decision with 18 saves.
Oliver-Ekman Larsson scored for the Coyotes, who fell for fifth time in six contests.
Mike Smith was lit up for all five goals on 38 shots.