The Nationals won two out of three in the series and handed Miami its ninth loss in 11 games.
Washington jumped in front with a two-run second, one of the runs coming on the sacrifice fly from Suzuki. He then hit a solo shot in the fifth.
Harper, who had missed Tuesday's 8-2 loss with flu-like symptoms, bounced back in a big way. He scored a run and drove in another in the ninth with an infield single.
Ross Detwiler (1-0) allowed the only Miami run on seven hits over seven innings. He did not earn a decision in either of his first two starts despite giving up only one run on 10 hits in 13 innings.
Ricky Nolasco (0-2) yielded four runs on seven hits in six innings.