The Nationals have won 11 of their first 15 games this season.
Detwiler (2-0) gave up three hits and walked one. Craig Stammen, Tyler Clippard and Henry Rodriguez worked an inning each in relief -- Rodriguez giving up two walks in the ninth before picking up his fourth save in as many opportunities.
Washington has played eight games this year decided by one or two runs and has a 6-2 record in those contests. Miami had a four-game winning streak snapped.
Carlos Zambrano (0-1) allowed only two hits and struck out six over seven innings, but still took the loss.