After John Tavares drove toward the net, a loose puck popped off the pads of Boston goaltender Jeremy Swayman and went to Knies, who potted it after charging down the slot.
Jake McCabe also scored and Joseph Woll made 27 saves in his first start of the series for Toronto, who will host Game 6 on Thursday.
Trent Frederic scored Boston's lone goal. Swayman made 31 saves but took his first loss to Toronto in seven meetings in 2023-24, including the regular season and postseason.
Predators 2, Canucks 1
Alexandre Carrier's third-period goal completed a comeback and Nashville extended their Western Conference first-round playoff series with a victory over hosts Vancouver in Game 5.
With the score tied and his team's season on the line, Carrier netted his first career playoff goal to put the Predators ahead with 7:14 remaining in regulation. Roman Josi also scored for the Predators, who still trail the best-of-seven set 3-2. Game 6 will be played Friday in Nashville.
Nikita Zadorov scored for the Canucks, the Pacific Division champions. Goalie Arturs Silovs stopped 20 shots.
Avalanche 6, Jets 3
Mikko Rantanen had two goals and an assist as Colorado eliminated hosts Winnipeg in Game 5 of a Western Conference first-round playoff series.
Valeri Nichushkin and Artturi Lehkonen also scored for the Avalanche, making them the first teammates in NHL history to score at least one goal apiece in a team's first five postseason games. Colorado will play either the Dallas Stars or the Vegas Golden Knights in the conference semifinals. Alexandar Georgiev made 34 saves.
Kyle Connor, Josh Morrissey and Tyler Toffoli scored and Connor Hellebuyck stopped 27 shots for the Jets.
Hurricanes 6, Islanders 3
Jack Drury and Stefan Noesen scored eight seconds apart in the third period as Carolina emerged from a tie and earned a series-clinching victory against New York in Game 5 of a first-round playoff series in Raleigh, N.C.
The Hurricanes won the Eastern Conference series 4-1, earning a date with the Presidents' Trophy-winning New York Rangers in the next round. Brady Skjei assisted on both goals, and Frederik Andersen made 22 saves.
Brock Nelson had a goal and an assist, Mathew Barzal and Ryan Pulock each had two assists and Semyon Varlamov made 32 saves for the Islanders. Mike Reilly and Casey Cizikas had New York's other goals.