Drummond's dunk on an alley-oop from Will Bynum made it 89-73.
"I just always move myself into the right areas," Drummond said. "Try to get behind the defense. For the most part, we all click as a team."
Monroe, Knight and Bynum scored 15 points apiece for Detroit. Courtney Lee had 16 for Boston, and Jeff Green added 15.
Celtics guard Avery Bradley was back after missing a game with a rib injury, but he scored only six points.
"I had double pads on just in case I got hit while I was in the game," Bradley said. "I just have to fight through it."
The Pistons arrived back from overseas around midday Friday.
"If we're going to search for excuses, they'll always be there," Frank said before Sunday's game.
But Detroit looked fine from the start. The Pistons scored the game's first seven points and then went on a 9-0 run at the beginning of the second quarter to take a 36-18 lead.
"Just getting back in the gym after getting back from London and getting that jet lag out of there and get some shots up — we got some great workouts in," Knight said.
Boston responded after falling behind by 18, scoring the game's next 10 points, including a steal and dunk by Paul Pierce and two 3-pointers by Lee. Twice, the Pistons turned the ball over near their own free throw line after defensive rebounds, leading to easy baskets for the Celtics.
Boston finally tied it at 48.
NOTES: The Celtics have lost four straight to Detroit. ... The Pistons had 21 turnovers and Boston had 18. ... Monroe, Knight, Bynum and Kyle Singler had five assists apiece for Detroit.