The Celtics clinched the best-of-seven series with victory in Game Six and advanced to the Eastern Conference final, where they will play the Orlando Magic, who have not lost since April 2.
Veteran Boston forward Kevin Garnett led the home team with 22 points and 12 rebounds, and received support from guard Rajon Rondo with 21 points and forward Paul Pierce with 13 points.
"Winning is gratifying. You're playing the best team in basketball. But one thing we don't lack is confidence," the 33-year-old Garnett told reporters.
The Celtics never trailed by more than four points and appeared to break the game open late in the third quarter, when Rasheed Wallace and Pierce converted three-pointers about 30 seconds apart to build a 12-point cushion.
Still, there was always the spectre of Cleveland's two-time league MVP LeBron James, who slotted two three pointers early in the fourth quarter to narrow the deficit to four points and the Cavaliers seemed on the verge of turning the tide.
The Celtics, however, took a time-out, regrouped, and went on a 10-0 run to end the fight back.
"They started to grab the momentum ... but throughout the whole series when we ran up against some tough times we held it together," said Garnett.
The 25-year-old James, who ended with 27 points, 19 rebounds and 10 assists, is one of a number of high-profile players who could opt for free agency this year.
Media speculation is growing he may leave the Cavaliers after failing again to win the title and Boston fans chanted "New York Knicks, New York Knicks" when he lined up for free throws, amid rumours he might head to the lowly New York team.
"I've made no plans," James said. "The fact that (the season) is over right now is certainly a surprise to me."
Cleveland coach Mike Brown said speculation about James' future had not distracted his team, on or off the court.
Celtics captain Pierce said beating the Cavaliers was not enough to make Boston's year complete.
"The only thing that's going to make our season is to win the championship," Pierce said.
"We'll get excited when we put that banner up."
