Kostitsyn also assisted on Alex Tanguay's second-period power-play goal.
Goaltender Jaroslav Halak made 18 saves on 19 shots and Montreal earned a split of the first two games at the start of its 100th NHL season.
The Buffalo Sabres beat the Canadiens 2-1 in a shootout Friday night.
The Maple Leafs scored on Jason Blake's power play at 11:02 of the second period.
Toronto goalie Vesa Toskala was beaten six times on 23 shots before Curtis Joseph replaced him in the third period.
Joseph stopped the 11 shots he faced.