The Pistons collected an overwhelming 27 offensive rebounds and won the battle of the boards 63-41.
Detroit pulled away down the stretch to snap a six-game losing streak and hand the 76ers their third loss in a row.
Smith scored 22 points, grabbed 13 rebounds and blocked five shots. He came within three assists of a triple-double.
Brandon Jennings was one of seven Pistons to reach double figures, scoring 19 points. Will Bynum and Kyle Singler both had 16 while Drummond collected 16 rebounds to go with his 11 points and six blocks.
Thaddeus Young collected 22 points for Philadelphia and Michael Carter-Williams scored 21.