DeMar DeRozan had 13 points and Terrence Ross added 12 for the Raptors.
Gerald Wallace led the Celtics with 16 points, and Jared Sullinger had 14 with six rebounds.
The 36-year-old Stevens was hired in July after a successful run at Butler University.
"Really, really different just because it's a 48-minute game, something to get used to because of the timeouts," Stevens said. "It's a little unique and different. There's eight more minutes (than college) and a lot more possessions because of the 24-second shot clock. Hopefully I'll get used to it in seven (preseason) games, but hopefully it doesn't last much longer than that. But it is different. It's unique."
The Celtics had seven new players, mainly due to a blockbuster deal that sent likely future Hall of Famers Paul Pierce and Kevin Garnett to the Brooklyn Nets in a draft-night deal. GM Danny Ainge wanted to start rebuilding the team before the two became ineffective or retired.
Ainge also traded coach Doc Rivers to the Los Angeles Clippers for a first-round draft pick during the off-season.
The Raptors also made a big trade during the off-season, sending Andrea Bargnani to the New York Knicks in early July for three players and three draft picks.
"Turnovers," Raptors coach Dwane Casey said of his team's play. "You see we turned it over 25 times. I know it's an exhibition game, but we've got to get that way down."
The teams will face each other in the season opener in Toronto on Oct. 30.
Boston point guard Rajon Rondo is expected to miss at least the season's first month after undergoing surgery for a torn ligament in his right knee last season.
"As a team, I felt like we moved the ball well," said guard Avery Bradley, who will run the team in Rondo's absence.
The game was tied at 84 midway into the fourth before the Raptors pulled away with an 11-3 run.
"At the end of the game when we had a chance to cut into it, I thought we got pretty good looks," Stevens said. "And it's the first exhibition game, so we'll see if those go down as we move forward."
Boston trailed 67-58 in the third, but scored 15 of the next 21 points, tying it on Wallace's basket.
The Celtics' debut under Stevens didn't get off to a good start. They missed their first seven shots from the field and didn't score their first point until Kris Humphries' foul-line jumper nearly 4 minutes in.
Boston had only six rebounds in the first half.
Toronto led 14-2 in the opening 7 minutes.Suggest a correction