The forward scored at 11:55 of the second period for Ottawa's third goal. He had two assists in the first period.
The top line for the Senators (Stutzle, Brady Tkachuk, Drake Batherson) combined for six points (three goals, three assists). Anton Forsberg made 20 saves.
Claude Giroux scored the go-ahead goal for Ottawa at 8:02 of the third period.
Kirby Dach scored his first goal with Canadiens, who have lost each of their seven preseason games (0-6-1). Cayden Primeau made 22 saves.
Batherson scored 38 seconds into the first after a pass from Stutzle to give the Senators a 1-0 lead.
Tkachuk made it 2-0 at 8:27 when he converted a 2-on-1 pass from Stutzle. Batherson had an assist on the goal.
Kaiden Guhle made it 2-1 at 12:23 when his rising point shot found its way through traffic.
Dach, who was acquired in a trade with the Chicago Blackhawks on July 7, tied it 2-2 with a power-play goal at 5:13 of the second period, scoring off a pass from Brendan Gallagher.
Josh Anderson made it 4-3 at 9:16 of the third when he converted a pass from Jujar Slafkovsky, the No. 1 pick in the 2022 NHL Draft.
Each team will end its preseason with a rematch at J.K Irving Center in Bouctouch, New Brunswick, for Kraft Hockeyville 2021 on Saturday (6:30 p.m. ET; TVAS).