Kelly Olynyk scored 18 points in as many minutes off the bench, while Rajon Rondo handed out 18 assists to go with 11 points for Boston, which closed out a successful homestand with back-to-back wins.
Kris Humphries also posted a double-double with 20 points and 11 boards, and Jared Sullinger totaled 14 and eight in a reserve role.
"I thought the ball movement was great tonight, I think we had a verity of guys tonight making shots and that always helps," said Celtics forward Brandon Bass.
The Pistons turned it over 16 times and dropped their third straight game despite double-doubles from Andre Drummond, Josh Smith and Greg Monroe. Drummond pulled down 22 rebounds and scored 18 points, Smith led all scorers with 28 points to go with 11 boards and Monroe netted 22 with 14 rebounds.
"We gave them too many easy baskets," Pistons head coach John Loyer said.
The Celtics scored the final six points of the first quarter to take a 26-22 lead, and they led the rest of the way.
Green's 3-pointer midway through the second extended the margin to 43-30, and Boston's 57-49 halftime lead was stretched to as many as 17 in the third after Green connected on consecutive 3-pointers and Jerryd Bayless added another from long range during a quick 9-0 run.
Detroit's Will Bynum opened the fourth quarter scoring with a three-point play that pulled the Pistons within 95-87, but an 8-0 Celtics run a little later made it a double-digit game again.
The lead was trimmed to four inside the final minute, but Boston made enough free throws to close out the win.