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.
Braves manager Fredi Gonzalez, who hinted he may tweak his slumping lineup, said an offensive turnaround is coming.
"Somebody's going to have to pay for it," Gonzalez said. "Sooner or later somebody's going to come in here and we're going to score 10 runs a game for two or three weeks. That's my mindset I've got going on right now."
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. 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.
Bumgarner has allowed only one earned run in winning three straight starts against the Braves, including two wins in 2013. ... Gonzalez said SS Andrelton Simmons was held out for personal reasons and 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.