Nolasco (12-12) surrendered four hits and a walk while striking out six in tossing his eighth career shutout and ninth career complete game.
He also contributed a two-run double while Greg Dobbs added three hits and a run scored in the win.
Giancarlo Stanton chipped in with a solo homer as the Marlins took the rubber match of a three-game series.
Nationals starter Edwin Jackson (9-10) was touched for six runs on nine hits over 4 2/3 innings.
National League East-leading Washington lost for just the second time in eight contests.