The Cavs, behind a masterclass from center Jarrett Allen, notched the franchise's fifth straight game-seven triumph as they vanquished the Raptors for the fourth time in four post-season meetings.
Cleveland erased an early 10-point deficit to go into halftime tied at 49-49 and opened the third quarter on a 9-0 scoring run.
They out-scored the Raptors 38-19 in the third, Allen scoring 14 of his 22 points and pulling down 10 of his 19 rebounds in the period.
"I just wanted to show my teammates that we can win this game," said Allen, who added two steals and three blocked shots.
His dominance on the boards helped the Cavs win the rebounding battle 60-33.
"Energy and effort, that's what I believe wins games," Allen said. "If you do it on the defensive end, everything translates to the offense.
"Every single possession, it means a lot," he added of the game-seven intensity. "Every single possession means it could be the end of the season."
Donovan Mitchell added 22 points for Cleveland and emerged unscathed from his own energetic leap for a ball which landed him in the third row of Rocket Arena seats early in the third quarter.
Veteran James Harden chipped in 18 points.
Scottie Barnes led the Raptors with a game-high 24 points, but Toronto's ability to respond in the second half took a hit when foul trouble sent him to the bench for extended minutes.