Top-seeded Boston, who were stunned by the Cavaliers at home in game two, edged the first quarter by two points and never relinquished their lead.
The Celtics now take a 2-1 lead in the best-of-seven series into game four in Cleveland tonight.
Jayson Tatum hit 33 points for the Celtics, while Jaylen Brown added 28.
“We just wanted to bounce back,” said Tatum. “Our back was against the wall, so it was a good test for us to see how we respond - we were up for the challenge.”
Donovan Mitchell top scored for Cleveland, with 33 points. Elsewhere, the Dallas Mavericks took a 2-1 lead in their Western Conference semi-final with a 105-101 win at home over the Oklahoma City Thunder.
PJ Washington led the Mavs with 27 points, while star guard Luka Doncic added 22.