Serge Ibaka scored 26 points and Kyle Lowry got 23 for the Raptors, but it was Norman Powell who made the difference at the end, scoring eight consecutive points in the final minute after Cleveland cut Toronto's lead to just one point.
Powell got a three-pointer, scored on a lay-up after making a steal and made three foul shots to seal the win.
Cleveland have now lost nine of their last 10 games and nine straight at home.
Before Boston's first home game after the death of Kobe Bryant in a helicopter crash last Sunday, his number 24 was illuminated in lights on the court as 24 seconds of silence were observed.
It was followed by a video tribute from current and former Celtics, and they secured a 119-104 win over the Golden State Warriors.
The Warriors have now lost five straight and remain rooted to the bottom of the Western Conference.
In Los Angeles, the Staples Center hosted its first game since Bryant's death.
The Kings were behind by five points at the end of the first quarter, but outpointed the Clippers 36-14 in the second to take a strong lead into half-time.