Bayless came off the bench to hit 6-of-10 shots and 9-of-11 from the foul line to lead five Grizzlies in double figures.
It was the fifth win for Memphis in seven games.
Boston was led by 26 points from Jeff Green, but the Celtics have lost seven out of nine.
Memphis took charge with a 15-2 run that closed out the first period, at the end of which the Grizzlies had a 27-13 lead.
Swim Week Miami Beach 2014 [PHOTOS]