Max Domi had three assists, Nicholas Robertson had a goal and an assist and Joseph Woll made 26 saves for the Maple Leafs (17-15-5), who have won two in a row after losing five of their previous six.
Toronto forward William Nylander, who also scored, left the game at 6:22 of the second period and did not return because of a lower-body injury.
Tim Stutzle scored to extend his point streak to nine games (eight goals, eight assists) and goal streak to four games (four goals), and Jordan Spence had a goal and an assist for the Senators (18-14-5), who were 3-0-2 in their prior five games. Linus Ullmark was pulled in the second period after allowing four goals on 14 shots. Leevi Merilainen made 16 saves in relief.
Bobby McMann gave the Maple Leafs a 3-2 lead at 3:28 of the second period when he poked in a loose puck behind Ullmark while standing at the side of the net.
Matthews extended it to 4-2 at 7:28, putting in a rebound in the slot after Ullmark juggled a point shot from Domi.
Robertson pushed it to 5-2 at 8:32 when he one-timed a pass from Knies past Merilainen’s left pad.
Drake Batherson scored 14 seconds into the third period to cut it to 5-3 14 seconds after he got behind Oliver Ekman-Larsson and took a pass from Dylan Cozens in the slot before shooting over a sprawling Woll.
Stutzle made it 5-4 at 5:07 when he pulled the puck off the half boards, cut into the slot and shot off Woll’s glove.
Knies put Toronto up 6-4 at 5:53. After Morgan Rielly cut to the net, he swung a pass into the slot for Knies, who dove to slide a backhand past Merilainen.
Spence cut it to 6-5 on his own rebound after his initial shot hit Claude Giroux at the top of the goal crease before shooting from the slot past Woll, who was out of position.
Tavares shot into an empty net at 18:44 for the 7-5 final.
Nylander’s power-play goal gave the Maple Leafs a 1-0 lead 40 seconds into the first period when he took a pass from Matthews to put him in alone on Ullmark before beating the Senators goalie with a backhand deke.
Knies scored on the power play to make it 2-0 at 14:42, one-timing a pass from Domi over Ullmark’s glove from the slot. The goal ended a nine-game drought.
Nick Cousins cut it to 2-1 at 17:50 when he put a rebound from Jordan Spence’s shot past Woll’s outstretched left pad.
Ridly Greig tied it 2-2 18 seconds into the second period when he outbattled Philippe Myers on a breakaway and got the puck on net. Myers fell while backchecking and ended up driving the loose puck into the net as he slid into Woll.
