Mitchell scored 23 of his 29 points in the second half and received plenty of support from aggressive teammates as the Cavs bounced back from a game-one rout.
Evan Mobley, 22, got Cleveland going early, scoring 15 of his playoff career-high 21 points in the first half. Mobley added 10 rebounds and five assists and reserve guard Caris LeVert added 21 points off the bench for Cleveland, who had six players score in double figures.
"I like the way that we were just attack-minded," Cavaliers coach J.B. Bickerstaff said. "We didn't settle for the first quick (shot) that we saw. We were attack-minded and understanding how they're playing with their space."
The Cavs fell behind in each of the first two quarters but finished both of them strong and had tied it up 54-54 at halftime.
Mitchell erupted for 16 points in the third quarter as the Cavaliers seized control, taking the first double-digit lead of the night for either team on Darius Garland's three-pointer midway through the period that put Cleveland up 77-66.
Cleveland finished with 13 three-pointers while Boston made just eight on 35 attempts. The Celtics, who led the league with 64 regular-season wins, were 0-for-8 from three-point range in the third quarter.
The Cavs, up by 12 going into the fourth, pressed their advantage, as Mitchell drained three straight baskets that included a spinning drive for a hook shot that made it 99-83.
By the time Tatum was called for a flagrant foul -- when his arm made contact with LaVert's head on a play that pushed Cleveland's lead to 24 points -- fans were streaming out of T.D. Garden arena.
Celtics coach Joe Mazzulla pulled his starters, with Tatum finishing with 25 points and Jaylen Brown adding 19.
"Everybody did their job," Mitchell said, heaping praise on Mobley, who started in place of injured center Jarrett Allen.
"To come out here on the road as a young player, that's a big-time performance to set the tone for us."
Now, Mitchell said, the Cavs need to keep the pressure on when the series shifts to Cleveland for game three on Saturday.
"At the end of the day, it's one win," Mitchell said. "We've got to do it at the crib."
In Western Conference action, the top-seeded Oklahoma City Thunder hosted the Dallas Mavericks, with the Thunder aiming to build on their game-one victory.
Dallas star Luka Doncic, playing through a right knee sprain, connected on just six of 19 shots from the field in game one. The Slovenian star, who led the league in scoring in the regular season, will be hoping to turn up the heat to help the Mavs level the series.
