Madison Bumgarner pitched six sharp innings as the NL West-leading Giants won their fifth in a row.
The Braves' skid is their longest skid since an eight-game slide in May 2012. Atlanta, which began the series leading the NL East, was held to one run in each of the losses to San Francisco.
Bumgarner (3-3) allowed one unearned run and three hits, striking out nine. He earned his first win since April 11.
Crawford gave the Giants a 2-1 lead with his homer off Alex Wood (2-5) in the fourth. Crawford hit a two-run shot off Jordan Walden in the eighth for his first career multihomer game. He began the day with only one homer this season.
Wood lost his fourth straight start, again receiving almost no run support. The one run scored by Atlanta on Sunday is the only offense Wood has received in that span, which included back-to-back 1-0 losses.
The left-hander has a 3.00 ERA after allowing two runs on seven hits and one walk in five innings.
The Giants' only runs in their first two wins of the series came on five solo homers. They found another way to score in the first when Hunter Pence hit a one-out double, moved to third on a wild pitch and scored on Buster Posey's grounder to first base.
Atlanta's Evan Gattis was called for catcher's interference on Posey's grounder, and the umpires initially ruled Posey was safe at first and Pence had to return to third base. Giants manager Bruce Bochy took advantage of Rule 6.08c, which allows a manager to take the live play instead of the interference ruling.
Jason Heyward hit a sacrifice fly in the Atlanta third. The Giants reclaimed the lead on Crawford's homer to right-center with two outs in the fourth.
NOTES: Bumgarner has allowed only one earned run in winning three straight starts against the Braves, including two wins in 2013. ... Braves manager Fredi Gonzalez said SS Andrelton Simmons was held out for personal reasons, but was available off the bench. Simmons is expected to start on Monday. ... Braves RHP Gavin Floyd (elbow surgery) came off the 15-day DL and will start on Tuesday against St. Louis as RHP Ervin Santana has his scheduled start skipped due to swelling below his right thumb. Gonzalez said he expects Santana to start on Saturday against the Cubs. ... The Giants open a series at Pittsburgh on Monday as RHP Matt Cain starts. ... The Braves' homestand continues on Monday night with RHP Aaron Harang facing Cardinals RHP Shelby Miller.