Mitchell scored 20 points in the fourth quarter as the Cavs rallied from 14 points down in the second half to defeat the reigning NBA champions.
The Cavaliers started the season 15-0 but suffered their first loss at Boston last month by 120-117 and dropped their two prior games, both losses to Atlanta, before staging a fightback home triumph.
"For us, we've got to go out there and make a statement," Mitchell said. "They beat us in the NBA Cup. No excuse. We've got to go out there and try to build. We had two losses that really hurt. We weren't playing like ourselves. We needed this win."
The Cavs improved to 18-3 to stay atop the Eastern Conference while the Celtics fell to 16-4 as Cleveland snapped Boston's seven-game win streak.
"You've got to trust your work and what we've been working on since training camp. That's the biggest thing," Mitchell said. "That's what you saw tonight and that's what it's going to continue to be."
The Celtics were without starting guards Jaylen Brown due to illness and Derrick White with a sprained right foot.
"Just because they've got two guys down, they've got a lot of guys who are capable," Mitchell said. "You've got to respect them. They're champions for a reason."
Cleveland led 51-49 at half-time but the Celtics dominated the third quarter for an 84-72 lead entering the fourth, Jayson Tatum scoring 17 of his 33 points in the third period to lead Boston.
Mitchell responded in the fourth, making a floater that gave the Cavs a 103-101 lead with 67 seconds remaining and concluded his run of 11 consecutive Cavaliers points.
"The biggest thing is you've just got to pick your spots, find your moments throughout the game," said Mitchell. "They kind of went on a run and in the fourth quarter I started to make my imprint."
Darius Garland, who had 22 points, joined Mitchell in hitting key free throws late to clinch the victory.
"We executed on both ends of the floor," said Mitchell. "I scored offensively but we were getting stops and finding ways to get rebounds, loose balls, different things. That's what ultimately ended up getting us the W."
Rockets defeat Thunder
In a battle between the Western Conference leaders, Fred VanVleet scored a season-high 38 points to lead the Houston Rockets over visiting Oklahoma City 119-116.
Houston improved to 15-6 but the Thunder, led by 32 points from Shai Gilgeous-Alexander, fell to 15-5.
Dillon Brooks made a steal and sank a jumper to give Houston a 115-113 edge with 33 seconds remaining and VanVleet added two free throws.
Oklahoma City's Jalen Williams sank a 3-pointer with 2.1 seconds to play but VanVleet's two final free throws sealed victory.
French star Victor Wembanyama had a triple double with 34 points, 13 rebounds and 11 assists to spark the San Antonio Spurs to a 127-125 victory at Sacramento.
At Salt Lake City, Anthony Davis had 33 points and 11 rebounds while LeBron James added 27 points and 14 assists to lead the Los Angeles Lakers to a 105-104 triumph over the Utah Jazz.
Luka Doncic returned after missing five games for Dallas with a wrist injury with game highs of 36 points, 13 assists and seven rebounds to lead the Mavericks to a 137-131 victory at Portland.
The Mavs were without Kyrie Irving due to a sore shoulder and Klay Thompson with a left foot injury.
Orlando's win streak stretched to six games as Franz Wagner scored 20 points, grabbed nine rebounds and passed off eight assists to power the Magic (15-7) over host Brooklyn 100-92.
Mikal Bridges scored 31 points and Karl-Anthony Towns had 14 points and 19 rebounds to spark the host New York Knicks over New Orleans 118-85.
Toronto's R.J. Barrett scored 37 points and Toronto beat visiting Miami 119-116 while Jaren Jackson led Memphis with 25 points as the host Grizzlies beat Indiana 136-121.