Grabovski also assisted on Matt Fratin's second-period equalizer for the Leafs, who logged a win in Randy Carlyle's first game as coach after replacing the fired Ron Wilson.
Jonas Gustavsson turned aside 21-of-22 shots for Toronto, which pulled to within three points of the eighth and final Eastern Conference playoff slot.
Reeling Montreal, meanwhile, fell for the sixth time in seven contests.
Erik Cole scored and Carey Price made 39 saves for the Canadiens.
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