Wood (5-5) struck out eight, walked none and allowed five hits for the Braves, who snapped a five-game losing streak. Jace Peterson smacked a solo homer in the triumph.
The Pirates put the tying run on second with two outs in the ninth, but Jason Grilli struck out Gregory Polanco to end the game and notch his 21st save of the season.
Jeff Locke (4-4) surrendered a run on five hits and three walks over five frames for Pittsburgh.
The Braves scored a run in the fifth and added another in the seventh.
Cameron Maybin hit a two-out single, advanced to second on a passed ball and scored on Nick Markakis' roller through the hole on the right side. Peterson's leadoff blast to center in the seventh made it 2-0 in favor of Atlanta.
The Pirates had registered just a pair of singles in the first six innings and didn't threaten until the home seventh.
Pittsburgh had runners on second and third with two one out, but Wood struck out Jordy Mercer and induced an inning-ending pop out off the bat of Sean Rodriguez.
Mercer's RBI double in the ninth finally got the Pirates on the board.