A bit later in the first, with Toronto pressing and Montreal unable to clear, Auston Matthews blasted a one-timer past Carey Price to square things up.
In the dying minutes of the period, Trevor Moore stole the puck behind the net and sent it to Alexander Kerfoot, who beat Price with a wrister to put the home team up 2-1.
In the second, Kerfoot escaped on a breakaway but had multiple attempts of his denied by Price.
Not long after, however, Trevor Moore accepted a pass from Ilya Mikheyev on a 2-on-1 and buried it to double the Leafs' lead.
After 40, the Leafs were outshooting the Habs 25-21 and leading 3-1.
In the final frame, with Phillip Danault in the box, William Nylander wristed it past Price to up the score to 4-1.
On the ensuing play - before the Leafs' goal was even announced - the Canadiens took advantage of a turnover in the neutral zone and Jonathan Drouin managed to get the puck past Leafs starter Michael Hutchinson to cut Toronto's lead back down to two.