Zimmerman touched off a four-run first inning with a two-run double and added a solo shot in the fifth to make it 5-1 Washington.
The Nats' third baseman added a run-producing single in the ninth while Adam LaRoche and Jhonatan Solano each contributed an RBI in the victory, which gave National League East-leading Washington the rubber match of a three-game set.
Gio Gonzalez (11-3) became the NL's first 11-game winner despite allowing four runs on five hits in a five-inning effort. The Nats' bullpen secured the win with four innings of shutout relief.
The Braves' Tim Hudson (6-4) was tagged with the loss, surrendering six runs (five earned) on eight hits over six full frames.
Freddie Freeman smacked a three-run homer for Atlanta.