Zimmerman connected for a two-run shot in the second inning and solo homer in the third, giving the Nationals a 3-0 lead.
Roark (5-0) scattered four hits in his first major league start and didn't issue a walk in a dominating performance, striking out four. The rookie has posted a 0.94 ERA in his first 10 big league appearances.
Marlins starter Nelson Eovaldi (3-6) was reached for five runs on nine hits in a three-inning stint.
Adeiny Hechavarria and Jeff Mathis each drove in a run for Miami.