Terry Rozier scored 18 points, Al Horford added 15 points and 10 boards, Marcus Morris had 12 points and both Jayson Tatum and Marcus Smart contributed 11 for the Celtics, who were 108-83 winners Sunday in Game 1.
LeBron James recorded 42 points, 12 assists and 10 rebounds for the Cavaliers, marking his NBA-record 17th career playoff game with 30 points and 10 assists. Kevin Love added 22 points and 15 rebounds, but Kyle Korver (11 points) was the only other Cleveland player to score in double figures.
James, who managed just 15 points in the Game 1 loss, has won five consecutive East playoff series after losing the series opener.
Boston, which improved to 9-0 at home this postseason, has never lost a best-of-seven playoff series when leading 2-0.
"We just play hard," Horford said. "We go out there, we compete. It's Celtics basketball. We're really embracing Celtics basketball. We're playing hard.
"We've got each other's backs, and that's it."
Game 3 is Saturday night in Cleveland.
"We have an opportunity to go back home, protect home court," James said. "We're going to use these days to really dive in on what needs to be done to help our ballclub be successful.
"They did what they had to do, and that was protect home, and now it's our time to try to do that as well."
Smart's 3-pointer with 4:34 left in the third quarter gave the Celtics a 72-71 lead after they had trailed by 11. It was their first lead since they were up 3-2 only 49 seconds in. Boston was on top 84-77 entering the fourth quarter.
Greg Monroe's cutting layup with 11:14 remaining put Boston up by 11. Neither team scored again until James' reverse layup with 9:08 on the clock.
Tensions boiled over when Cleveland's JR Smith shoved Horford on a drive to the basket. Smart and Smith exchanged shoves and had to be separated, with each player being whistled for a technical foul.
Horford's jump shot with 2:54 remaining pushed the Celtics' advantage to 103-89. After a James layup, Rozier tossed in a layup to make it a 14-point game. Cleveland waved the white flag and emptied its bench after that.
The Cavaliers led 55-48 at halftime.
James briefly exited with 3:48 remaining in the second quarter after being hit in the face by an inadvertent shoulder from Tatum under the basket, but he returned with 1:57 to play in the half. James was diagnosed with a strained neck.
James and Brown combined for 35 of the game's first 50 points as the Cavaliers jumped out to a 27-23 lead after one quarter.
Celtics coach Brad Stevens said of the team's approach to defending James, "I think the biggest thing is we're just trying to make it as hard as possible. ... We've got a lot of different guys guarding him.
"Jaylen started the game on him, Morris is guarding him a ton. I thought Semi (Ojeleye) did a good job on the couple of possessions he guarded him, which is really hard to just come off the bench not in the flow of the game and put a body in front of him, but he's unbelievable."
Cleveland coach Tyronn Lue said, "We'll be better going back home. We know that. They played well in that second half, and we've got to be ready to go on Saturday."
Before the game, the Cavs landed this year's eighth overall pick as the NBA held its draft lottery. Cleveland acquired the selection, which originally belonged to the Brooklyn Nets, in the trade that sent Kyrie Irving to Boston last offseason.
--Gethin Coolbaugh, Field Level Media