Floyd gave the Cubs a three-run cushion in the third inning. Former National Alfonso Soriano added two hits and scored twice as the Cubs improved to 5-and-0 versus the Nationals this season.
Zambrano is 10-and-6 after winning his third consecutive start, holding the Nats to a run and three hits over six and two-thirds. Zambrano struck out eight and blanked Washington until Ronnie Belliard hit a sacrifice fly in the fifth inning.
Tim Redding was a loser in his first major league appearance since 2005, allowing three runs and five hits in five innings.
Bobby Howry got the last two outs for his third save.