James hit an off-balance floater as time expired to seal a 105-103 win for the Cavs on Saturday at home in Quicken Loans Arena.
James finished the game with 38 points, six rebounds, seven assists and three steals.
This is the second time this postseason the four-time MVP hit a game-winner. His three-pointer was the difference in the Cavs' Game 5 win over the Indiana Pacers in the first round.
With Sunday's victory, Cleveland takes a 3-0 series lead over Toronto in the second round. No team has ever overcome a 3-0 deficit in the NBA playoffs.