After Ryan Zimmerman's leadoff homer in the second inning, the 42-year-old Dickey gave up only one hit — a two-out single by Trea Turner in the third — over the next five innings. Turner was picked off first base.
Dickey (10-10) gave up two runs, four hits and no walks. He made a strong case that the Braves should pick up his $8 million club option for 2018.
Zimmerman lined his homer into the left-field seats, tying the game at 1. He set a career high with his 34th homer, his fourth off Dickey this season.
Arodys Vizcaino struck out the side in a perfect ninth for his 12th save in 15 chances.
The Braves scored two runs in the fourth off Tanner Roark (13-10).