So somehow, Heyward contorted his big body to elude the tag and score a run that started a big inning for Atlanta.
"It was a reaction," Heyward said. "It's not the way you draw it up. I by no means would like to try it again as far as me running home and see the ball flying in from right field that far ahead of me. Just a hustle play and it worked out."
Evan Gattis drove in a run with his first career triple before Freddie Freeman, B.J. Upton and Andrelton Simmons hit RBI singles in the sixth against Ryan Vogelsong (1-2) to help the Braves win for the fourth time in five games.
The big inning never would have happened without some aggressive baserunning by Heyward, who advanced to second on a deep flyout before scoring with an athletic play on Freeman's single to right.
Hunter Pence's throw home easily beat Heyward, who ducked under the tag attempt and dove across the plate for a key run.
"Somehow he gets his big, 6-foot-5 body to go 5-foot-2 and get by Posey," Braves manager Fredi Gonzalez said.
Posey knew immediately that he missed the tag and didn't even try to argue. Giants manager Bruce Bochy challenged the play anyway, but umpire Ed Hickox's call was confirmed on replay.
"You don't have time to think, it's happening so fast," Posey said. "I caught the ball and saw him in front of me and I went and made a tag. I should have jabbed a little bit more. It does seem more guys are getting creative with their slides, more so than in the past. You don't expect a big guy like that to move like he did."
That play loomed even larger when Upton and Simmons hit two-out RBI singles that made it 4-0, giving Minor (1-2) more than enough support to end an eight-start winless streak dating to last season. He allowed three hits and two walks in 6 2/3 innings, striking out six.
Minor, who missed the first month this season with a sore left shoulder, pitched around a one-out double by Pence in the first inning and didn't allow another baserunner until Angel Pagan's two-out walk in the sixth as he shut down a Giants lineup that hit eight homers in the first four meetings with the Braves.
Minor gave up two of those in a 2-1 loss at home on May 2, but yielded nothing in the rematch, retiring 16 batters in a row at one point.
That stretch ended when Pagan walked and went to third on Pence's second double of the night. Minor struck out Posey to end the threat.
"For the most part I didn't think they knew what was coming," Minor said. "We went in and out, up and down and threw all the breaking pitches."
Vogelsong matched his career high with eight strikeouts but was done in by the big sixth inning.
"He threw the ball well," Bochy said. "He should have fared better than what happened."
The Braves added another run in the seventh after a replay review overturned a call of an inning-ending double play. Freeman was ruled safe when replays showed reliever David Huff never touched first base, allowing Tyler Pastornicky to score.
Pagan left the game with a sore knee and will get a day off Wednesday. ... Atlanta is 14-0 when scoring first. ... Hector Sanchez started at first base for San Francisco for the first time in his career. ... Madison Bumgarner (4-3) will start the series finale for San Francisco against Julio Teheran (2-2) on Wednesday.