Shawn Matthias scored twice, including the go- 1 win over the Hurricanes.
Muller, who had been serving as head coach for the Milwaukee Admirals of the American Hockey League, took over for Paul Maurice after he was fired on Monday. Muller served as an assistant coach with Montreal for five seasons and was also head coach on the Canadian collegiate level.
Jeff Skinner had the lone tally for the Hurricanes, who have lost four straight games.
Cam Ward stopped 18-of-20 shots in defeat.