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.
Swim Week Miami Beach 2014 [PHOTOS]