Boston led by 17 heading into the fourth quarter, but the Raptors fought back within four heading into the final half minute.
Sullinger's two perfect trips to the line negated a 3-point shot by Toronto's Kyle Lowry that briefly kept the Raptors' hopes alive with 15 seconds to go.
The win was Boston's first of 2014. The Celtics had not won since Dec. 28, when they edged Cleveland by three.
Toronto had won three in a row to build a 4 1/2 game over Brooklyn at the top of the Atlantic Division. The Raptors were paced by DeMar DeRozan with 23 points and eight rebounds.