Caufield kept the puck on a 2-on-1 with Nick Suzuki and scored on a slap shot from the right face-off circle to the far side.
Montreal had tied it with two goals in 1:05. Juraj Slafkovsky cut it to 5-4 at 15:36 of the third with his second of the game, deflecting a Lane Hutson point shot with Canadiens goalie Samuel Montembeault pulled for the extra attacker, before Alexandre Carrier’s one-timer from the top of the right circle tied it 5-5 at 16:41.
Caufield had two goals and an assist, Hutson had three assists, and Josh Anderson had a goal and an assist for the Canadiens (27-15-7), who had lost two straight. Suzuki had two assists, and Montembeault made 29 saves.
Jake Sanderson had a goal and three assists, and Tim Stutzle had a goal and an assist for the Senators (22-19-6), who had won two in a row. Leevi Merilainen made 13 saves in his 10th consecutive start.
Slafkovsky gave the Canadiens a 1–0 lead on the power play at 3:06 of the first period. From behind the net, Suzuki fed Caufield, who quickly slid the puck to Slafkovsky in the left circle for a one-timer over the glove of Merilainen.
Montreal’s Zachary Bolduc had a goal overturned at 11:30 after Ottawa challenged for offside.
Caufield made it 2-0 at 17:50 with the Canadiens back on the power play. After Suzuki won a puck battle against Claude Giroux near the left boards, he fed Caufield, who moved into the left circle and beat Merilainen with a wrist shot through the five-hole.
Brady Tkachuk scored the first of Ottawa’s four second-period goals, cutting it to 2-1 at 42 seconds during a 5-on-3 power play. Giroux got to the rebound of Sanderson’s shot in front of the net and passed to Tkachuk for a wrist shot in the left circle.
Stutzle tied it 2-2 at 3:07 of the second, scoring from in close with a high shot between his legs that went inside the left post.
Anderson regained the lead for Montreal, making it 3-2 at 4:26. He scored from the left point with a wrist shot through traffic.
Dylan Cozens then tied it 3-3 at 15:31, scoring with a wrist shot from the top of the slot off Stutzle’s pass out of the left corner.
David Perron gave the Senators their first lead of the game at 4-3 when Artem Zub’s shot deflected off his skate at 18:24.
Sanderson pushed it to 5-3 by scoring on the rush at 7:55 of the third.