The Raptors, who are languishing three places off the bottom of the Eastern Conference, grabbed only their 10th win of the season after stifling Boston's offense at the Scotiabank Arena.
Barrett spearheaded a balanced offensive display by Toronto, spreading the ball deftly as all five Raptors starters finished in double figures.
The win came as sweet revenge for Toronto, who had been on the receiving end of a brutal 125-71 mauling by the Celtics in Boston on December 31st.
"It was a tough loss for us in Boston," Raptors head coach Darko Rajakovic said afterwards.
"This group is very connected and is a very prideful group - so we really wanted to go out there and compete at the highest level. Everybody contributed tonight."
Barrett, who also had 10 rebounds and eight assists, was given scoring support from Scottie Barnes with 18 points, while Jakob Poetl finished with 16 points and 11 rebounds.
The Raptors defense meanwhile kept Boston star Jayson Tatum quiet, restricting the Celtics ace to just 16 points from 5-of-15 shooting.
Toronto improved to 10-31 in the Eastern Conference standings, while Boston dropped to 28-12 to fall 6.5 games behind leaders Cleveland (34-5) at the top of the table.
Nuggets struggle
Elsewhere Wednesday, the Denver Nuggets were humbled 128-108 at home by the high-flying Houston Rockets in a lopsided Western Conference duel.
The Nuggets suffered a blow before tip-off when three-time NBA Most Valuable Player Nikola Jokic was ruled out with an elbow injury during the warm-up.
With Aaron Gordon (calf) also missing, Houston rammed home their advantage to score a wire-to-wire victory. Jalen Green led the Rockets scoring with 34 points including six three-pointers.
Houston's fifth straight win leaves them in second place in the West on 27-12.
Denver coach Michael Malone said his team had failed to rise to the challenge following the injury absences of Jokic and Gordon.
"When you're without your starting power forward and center, against a team sitting No.2 in the Western Conference, you've got to play damn near perfect," Malone said. "And we were definitely far from that tonight. Just a disappointing night overall."
In other games on Wednesday, Stephen Curry drained seven three-pointers in a 31-point performance to help the Golden State Warriors grind out a 116-115 win over the Minnesota Timberwolves in Minneapolis.
In Philadelphia, Jalen Brunson's 38-point masterpiece helped the New York Knicks edge past the Philadelphia 76ers 125-119 in an overtime thriller at the Wells Fargo Center.
Mikal Bridges added 23 points while Josh Hart delivered a triple-double comprised of 10 points, 17 rebounds and 12 assists, with four steals thrown in for good measure.
The Knicks improved to 27-15 to remain third in the East while the Sixers, missing the injured Joel Embiid once again, fell to 15-24, just outside the play-off berths.
In San Antonio meanwhile, Victor Wembanyama produced a monster defensive performance but it was not enough to prevent the Spurs suffering a 129-115 defeat to the Memphis Grizzlies.
French star Wembanyama made eight blocks and hauled down 12 rebounds in vain as the Grizzlies remained in third place in the Western Conference on 26-15, eight games adrift of leaders Oklahoma City (33-6).
Ja Morant was the Grizzlies talisman, finishing with 21 points, 12 assists and four rebounds. Desmond Bane also had 21 points for the visitors.
In New Orleans, Dejounte Murray's 30 points propelled the Pelicans to a 119-116 win over the depleted Dallas Mavericks, who remain without injured stars Kyrie Irving and Luka Doncic.