The Cavaliers won 125-103 to put the pressure on the Raptors who host the third game on Friday.
James went into game two of the series 24 points adrift of second placed Kareem Abdul-Jabbar on the NBA's all-time play-off scoring list.
He surpassed Abdul-Jabbar's tally of 5,762 points with a three-pointer in the third quarter. James now sports 5,777 points and only Jordan on 5,987 stands before him.
"I have taken advantage of the opportunity I have been given," said James. "It was always my dream as a kid to be part of this league. I saw I had a gift and I didn't take it for granted. And I still don't even at 32.
"I have been in this league for 14 years. I've had some great teammates, I have been in the post-season for 12 straight years so those guys and coaches I've had have put me in positions to be successful."
"When you hear a name like Kareem -
He paid tribute to Abdul-Jabbar, who won six NBA championships between 1971 and 1988 and still found time play role in the film Airplane.
"I didn't actually get a chance to watch him play when I was growing up but I have read about his accomplishments," he added.
James has been enjoying a superb play-off, averaging 33.2 points, 9.8 rebounds, 8.0 assists, and 2.6 steals per game. While James has eclipsed Abdul-Jabbar with his post-season points prowess, he lags well behind him in regular season scoring.
Abdul-Jabbar is first on the all-time scoring list boasting 38,387 points while James is slouching back in seventh with 28,787 points.