The Nationals took a 5-1 lead through two innings and held on to complete a two-game sweep of the Tigers. Washington has won four in a row overall and six of seven.
Zimmerman and LaRoche both singled in a run in the second and Zimmerman scored one of Washington's three runs in the first on a base hit by Ian Desmond.
Dan Haren (4-3) picked up the win despite allowing nine hits over six innings. He enjoyed a 5-1 cushion heading into the sixth, but gave up a three-run homer to Matt Tuiasosopo in that frame.
Rafael Soriano allowed a two-out single in the ninth and nothing more while collecting his 12th save.
Doug Fister (4-1) suffered the loss, surrendering five runs on eight hits in only three innings.