Danny Espinosa drove in three runs for Washington, two of them with a third-inning homer, but it was the work of Gonzalez that allowed the Nationals to dominate.
Gonzalez (2-1) struck out seven and walked two while throwing 112 pitches. The only run he allowed came on a homer by Joey Votto in the fourth.
Rafael Soriano worked the ninth for Washington in a non-save situation.
Denard Span had three of the Nationals' 12 hits. He drove in a run with an infield single in the second and tripled in two more in the eighth.
Washington took control with a four-run third, which Espinosa finished off with his two-run blast.
Bronson Arroyo (2-2) took the loss, giving up six runs on nine hits in six innings.