Strasburg (12-5) scattered three hits while not allowing a runner to reach third base. The right-hander issued one walk and struck out six, increasing his major league-best total to 160.
Strasburg also put the Nats ahead to stay with second-inning single, scoring Jayson Werth and Danny Espinoza. The Washington pitcher and Steve Lombardozzi then each came home on Adam LaRoche's hit for a 4-0 lead.
Drew Storen tossed a scoreless ninth for his first save as the National League East-leading Nationals took three of four games in their series with the Marlins.
Miami's Ricky Nolasco (8-11) absorbed the loss, yielding four runs on eight hits over six full innings.
Greg Dobbs went 2-for-4 with an RBI in the loss.