Caufield made it 1-0 on Montreal's first shot of the game at 1:58 of the first period.
Chiasson tied it 1-1 at 8:35 when his shot deflected off Canadiens forward Jake Evans and went under Primeau's arm.
Suzuki scored a shorthanded goal to make it 2-1 at 9:58, shooting under Smith's glove on a 2-on-1. It was the Canadiens' ninth shorthanded goal this season, which tied the Boston Bruins for the most in the NHL.
Ryan Nugent-Hopkins tied it 2-2 at 10:53 on that power play before Draisaitl scored again on the man-advantage to give Edmonton a 3-2 lead at 10:47 of the second period.
Draisaitl, who is second in the NHL behind McDavid with 83 points (31 goals, 52 assists), extended his multipoint streak to seven games (seven goals, nine assists).
Suzuki tied it 3-3 at 8:22 of the third period when he redirected a centering pass from Caufield.
"I thought we had a great game, creating a lot," Suzuki said of playing with Caufield. "The chemistry is going to keep getting better and he sees the ice really well. He's always ready to shoot, and I like playing with guys like that."
Kahun won it on a breakaway off a pass from Draisaitl. Tyson Barrie, who had an assist on the play, has scored 48 points (eight goals, 40 assists), passing Adam Fox of the New York Rangers for the most among NHL defensemen.
"[Barrie] makes a lot of plays from the back end and playing with the top two lines at 5-on-5," Chiasson said. "So he's been a key player for us all year, and he will be a key player for us also going into the playoffs."
NOTES:Edmonton ends its regular season against the Vancouver Canucks on Saturday. ... McDavid leads the NHL with 71 assists. He is the first player to get at least 70 assists in 55 games or fewer since Mario Lemieux of the Pittsburgh Penguins had 70 assists through 50 games in 1995-96. … Since March 6, McDavid has more assists (29) than any player has points. … Draisaitl leads the NHL with 15 power-play goals and a plus-31 rating. Wayne Gretzky is the only player in NHL history to lead the NHL in power-play goals and plus-minus in the same season since plus-minus became an official statistic in 1959-60. Gretzky scored 20 power-play goals and was plus-78 in 1983-84. … Canadiens forward Jesse Ylonen had one shot on goal in 11:23 of ice time in his NHL debut.