The Nationals overcame a four-run deficit to force extra innings, but they eventually had a five-game winning streak snapped.
Reyes had another RBI triple in the fourth that gave Miami a 6-2 lead.
Chad Gaudin (3-1) worked the ninth for Miami to get the win. Despite giving up a run in the 10th and leaving the bases loaded, Steve Cishek picked up his 13th save.
Stephen Strasburg started for the Nationals and was roughed up for five runs on six hits in three innings without figuring in the decision.
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