Toronto produced a big third period that brought the Raptors back from a five-point deficit to a 10-point lead, but Boston then staged a comeback of its own to win its fifth in a row.
The Celtics' run of success has followed a six-game losing streak.
Boston outscored Toronto in the fourth quarter 30-16 with Kevin Garnett scoring 27 points to go with 10 rebounds. Courtney Lee came off the bench to score 15 points for Boston while Paul Pierce had 12 points, 11 rebounds and six assists.
The Raptors, who have lost 10 out of 13, were led by Rudy Gay with 25 points and 12 rebounds.
Boston's winning streak has lifted the Celtics two games over the breakeven mark. The Celtics evened their record against Atlantic Division opponents at 5-5.