Toffoli one timed a cross-crease feed from Cole Caufield to score his 4th goal of the playoffs and register the series winning goal.
Toffoli also had an assist on Montreal's first goal.
Erik Gustafsson and Artturi Lehkonen also scored for the Canadiens, who won their 7th straight playoff game.
Nick Suzuki had a pair of assists for Montreal.
Carey Price stopped 14 shots for Montreal, who will face the winner of the Colorado Avalanche/Vegas Golden Knights series which is tied at two games apiece.
Logan Stanley scored twice for the Jets, who were missing No. 1 centre Mark Schiefele, who was suspended for four games for charging Jake Evans in game one.
Connor Hellebuyck made 39 saves for Winnipeg.
SHOTS-WINNIPEG 16 MONTREAL 42
NOTES-Montreal D Jeff Petry did not play after suffering an upper body injury in game 3 and was replaced by Alexander Romanov who made his Stanley Cup playoff debut.