Heyward's homer in the third inning provided an early advantage for Minor, who proved strong on the mound and effective at the plate. He drew a seven-pitch walk to begin the three-run third inning and then damaged Bumgarner again with a seventh-inning double that put him in position to score the game's decisive run on Michael Bourn's two-out single.
Minor allowed a pair of seventh-inning hits, including Brandon Belt's two-out double before exiting with runners on second and third. That prompted the entry of Chad Durbin, who then surrendered a two-run double to Gregor Blanco before ending the inning with the Braves clinging to a 4-3 lead.
Instead of extending the frustration that had built as they lost six of their previous seven games, the Braves showed patience and added to their lead in the eighth inning courtesy of consecutive two-out bases-loaded walks Jeremy Affeldt issued to Bourn and Martin Prado.
"Every win is good, most definitely," Heyward said. "You don't want to compound things when they are not going as well, because that is what happens during the season. You're going to go through stretches where you don't hit well or don't pitch well."
Minor's offensive contributions helped end a maddening trend. The Braves had not scored a run while he was pitching since giving him a 6-0 second-inning lead before a lengthy rain delay limited him to 3 2/3 innings against the Marlins on Aug. 2. They had totaled one run or been shut out in five of his starts this season.
Throw in the fact the Braves had hit .197 over their previous seven games, and there was not a lot of reason for optimism leading up to this matchup against Bumgarner, who had posted a 1.93 ERA over his previous eight starts.
But Heyward set the tone for the afternoon when he made Bumgarner pay for the walks issued to Minor and Prado in the third inning. The 23-year-old outfielder sent a 1-0 fastball just over the top of the tall right-field wall. The three-run home run gave the Braves a lead they would not relinquish.
"I just got out of whack, mechanically and mentally both," Bumgarner said. "I never really got back to where I needed to be."
Heyward has hit five home runs in 34 career at-bats at AT&T Park. The only other visiting park where he has produced similar success is Wrigley Field, where he has four home runs in 31 at-bats.
"The crowd always keeps you on your toes here," Heyward said. "It's a good environment to play in. They're out there every night. It's a good team. They've got good pitchers. You've got to go up there focusing during every at-bat."
Minor limited the Giants to one hit -- Marco Scutaro's first-inning single -- through the first four innings. After a Joaquin Arias double put runners at second and third with no outs in the bottom of the fifth inning, the young left-hander maintained his poise and limited the damage to Belt's RBI groundout.
When Minor exited June with a 6.20 ERA, the Braves feared for the worst during these situations. But the young left-hander has earned his team's confidence while posting a 2.50 ERA over his past nine starts.
"Earlier on [in the season], that becomes a three-run homer," Braves manager Fredi Gonzalez said. "Today he minimized the damage and knew what he was doing. It's definitely nice to see him get through those innings."
While Minor had reason to be proud of his work on the mound, he might spend the next few days boasting about his offense. His seventh-inning double off the right-field wall was his third career extra-base hit and first since June 21, 2011.
"A lot of it I think was luck, but I did work a little bit with [hitting coach Greg Walker] just about approach," Minor said. "I've always been late. So I was like today I'm going to be early and try to drive the ball to right field. It happened that way. But I'm not saying I can do that every time."