Smith finished with 22 points overall and Rodney Stuckey came off the bench to put in 20 as Detroit claimed a third win in four games.
Greg Monroe contributed 12 points with 10 rebounds and Andre Drummond added 10 and 13 for the Pistons.
The Wizards got 34 points and six assists from John Wall but couldn't avoid the end of their three-game winning streak.
Martell Webster notched 15 and Marcin Gortat had a double-double of 10 points and 12 rebounds.
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