Drummond provided 15 points and 12 rebounds, while Monroe added 15 and 10 for Detroit, which won a second straight at home to begin the season.
Jennings missed the Pistons' first two games after having dental surgery. He was obtained from Milwaukee in an off-season trade.
Kelly Olynyk came off the bench to pace the winless Celtics (0-3) with 15 points and eight rebounds.
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