Jonas Gustavsson stopped 21-of-22 shots.
Erik Cole's first-period goal was all the offense for the Canadiens, who have dropped six of their last seven.
Carey Price played well in defeat, making 39 saves.
Grabovski's high wrister from between the circles with 8:15 left in regulation put the Leafs ahead 2-1.
Despite the one-goal deficit, Price did not leave the bench for an extra skater in the final minute. Cole was whistled for interference with 59 seconds to play and Frattin fed Grabovski for the insurance tally shortly into the advantage.
It was an inauspicious start for the visitors, as Cole lifted a rebound over a diving Gustavsson at the 7:16 mark of the first period.
But Toronto equalized 6 1/2 minutes into the second period. Grabovski won a right-circle draw, then while falling forward pushed the puck to Frattin for a quick one-timer.
Carlyle went 273-182-61 over 516 games with the Ducks from 2005 until this past November 30...Toronto has won three of five meetings against Montreal this season with one final matchup scheduled for the Bell Centre on April 7.