The victory ended a three-game losing streak for Boston and ended the Raptors' season-high five-game winning streak.
"When Rasheed puts his mind to it, he can be one of the best low-post players in the league," said Boston center Kendrick Perkins, one of just two regular starters in the lineup.
The other available starter -- Ray Allen -- made timely shots when things got tight.
"I thought we showed up with the attitude that we're going to find a way to win," Boston coach Doc Rivers said. "We didn't know how, but we're going to find it."
Paul Pierce missed his fifth straight game after having a pair of minor surgical procedures for an infection in his right knee, Kevin Garnett was sidelined for his second consecutive game because of a sore right knee, and Rajon Rondo was out with a sore left hamstring.
"Without their main players, they still go out there and play tough, play hard and play like they want to be a championship team," Toronto coach Jay Triano said. "You look at the numbers and it's a pretty good game, but I still don't think we played that well offensively. I didn't think we moved the ball very well."
Despite a makeshift lineup that had Allen starting at point guard and seldom used reserve Lester Hudson playing meaningful fourth quarter minutes, the Celtics opened an 83-71 lead on Hudson's jumper with 9:27 to play.
Toronto closed to within five points twice -- pulling to 88-83 on Bosh's left-handed hook with 4:11 to play -- but Allen nailed a jumper and Wallace drove in for a dunk to push the Celtics' lead to 92-83 with just over 3 minutes left.
After a Toronto timeout, Allen nailed a 3-pointer to move Boston ahead by 12. When the Raptors made one last push, cutting it to five with about a minute left, he took the ball up the floor, dribbled through the defense and in for a layup.
"We were just keeping it simple," Rivers said of the offense.
Boston led by 10 at the half and didn't see its lead fall below six in the third quarter. The Celtics entered the final quarter leading 78-67.
The Raptors came into the game holding teams to 86.8 points per game during their winning streak, but the Celtics found good offensive looks at key times and ran the floor to create fastbreak chances.
"Against this team, if you don't go inside and out you're probably going to shoot low percentage from the outside," Bosh said.
Boston opened a nine-point lead late in the first quarter before the Raptors closed to 29-27 heading into the second. The Celtics pulled ahead by 11 late in the second and held a 58-48 edge at halftime.
Toronto F Hedo Turkoglu, who left Wednesday's game against Charlotte at halftime with a bruised right knee, was back in the starting lineup. ... With Boston's rash of injuries, J.R. Giddens made his first professional start. ... Raptors G Jose Calderon missed his 10th straight game because of a sore left hip. ... Wallace and Turkoglu were whistled for matching technicals in the second. ... Boston came home after a 1/3 trip and will be back on the road for its next three.