The Maple Leafs fired Ron Wilson on Friday night and hired Carlyle, the former Toronto defenseman who was fired by Anaheim in December.
Matt Frattin also scored and Jonas Gustavsson made 21 saves to help Toronto end a six-game winless streak and win for only the second time in 12 games. Erik Cole scored for Montreal.
Grabovski made it 2-1 midway through the third period after the Maple Leafs caught Montreal on a line change. Clarke McArthur slid a pass to Grabovski, and the Belarusian center used Alexei Emelin as a screen to beat Carey Price with a high shot from the slot.
Grabovski added another on a power play with 53 seconds left.
Carlyle had said when he took over that the Leafs seemed tense, and nerves showed as Montreal controlled the early play and opened the scoring when David Desharnais fed Cole for an open shot 7:16 into the first.
Frattin tied it in the second period.
Notes: Scott Gomez and Aaron Palushaj both sustained eye injuries against Minnesota on Thursday night, forcing the Canadiens to call up Louis Leblanc and Andreas Engqvist from Hamilton of the AHL. ... Colby Armstrong sat out for Toronto. ... A fan fell from the middle tier of seats into the lower bowl before the game. A Canadiens spokesman said that while he — and the fan he landed on — were taken to a hospital, neither of the fans' injuries appeared to be life-threatening.