McCann matched his career high with five RBIs, helping the Braves end a rare two-game home losing streak by beating the Milwaukee Brewers 11-6 on Sunday.
The Braves, who won the series opener before losing two straight to Milwaukee, improved baseball's best home record to 32-12.
In Tuesday's All-Star Game, McCann's bases-loaded double drove in three runs. He was named the MVP of the National League's 3-1 win.
McCann's sixth career grand slam gave Atlanta a 7-1 lead over the Brewers in the third.
"Anytime you get the bases loaded, you want to get a big hit with less than two outs," McCann said. There were no outs when he hit the homer off Manny Parra on an 0-2 pitch.
McCann said he was thinking, "Better not miss this one. I'm lucky I didn't miss it."
Parra, a left-hander, said he made a mistake with a fat pitch to the left-handed hitting McCann.
"The pitch to McCann was right down the middle," Parra said. "I wanted to go up and in."
Two Atlanta batters were hit by pitches but both teams remained calm one day after Milwaukee's Prince Fielder was hit by a pitch, causing unrest in the Brewers' clubhouse.
Rickie Weeks had two homers and Fielder hit his second homer in as many days for Milwaukee.
By splitting the four games with Milwaukee, the Braves have lost only one of their last 20 series (15-1-4) since May 10. They are 41-20 in that span.
Home-plate umpire Scott Barry issued warnings to both benches when Parra hit Jason Heyward with a pitch in the sixth. The pitch hit Heyward's leg, and he calmly walked to first base.
"[Barry] said he didn't think he threw at him," Cox said. "It's amazing."
It was the second straight game in which a warning had been given to both teams. On Saturday night, Milwaukee manager Ken Macha was upset after Jonny Venters threw a pitch over Fielder's head and hit Fielder on his back with the next pitch. Venters and Cox were ejected.
Macha said he spoke with Bruce Froemming, a former umpire and current special assistant for Major League Baseball's umpiring department, about Saturday's incident and the high number of times his players have been hit by pitches.
Weeks' first homer was a blast over the center-field wall to lead off the game. Weeks set a career high and franchise record for a second baseman with 17 homers.
After Weeks' second homer in the sixth, Derek Lowe gave up three more hits, including Fielder's run-scoring single to cut Atlanta's lead to 8-3. Left-hander Mike Dunn ended the threat when Carlos Gomez hit into a double play with the bases loaded.
Lowe (10-8) became the first Braves pitcher with 10 wins. He gave up three runs on eight hits and a walk in 5 1/3 innings.
"Anytime you have a big lead, you'd like to go a little deeper than I did, but we were fortunate to have a lot of guys in the bullpen who were rested," Lowe said.
Diaz drove in Glaus with a double in the second. Atlanta's first five batters reached base in the third. Infante, who had four hits, had a run-scoring single before McCann's fifth career grand slam.
Diaz hit a homer in the fifth and a run-scoring single in the sixth, when the Braves finally knocked Parra out of the game with three runs.
Parra (3-7) gave up 10 hits and 10 runs, matching his career high, in 5 1/3 innings.
The start of the game was delayed by rain for 35 minutes.
Brewers rookie OF Lorenzo Cain had a pinch-hit single in the seventh for his first career hit and added a double in the ninth. ... Weeks previously shared the franchise mark for most homers by a Brewers' second baseman with Don Money, who hit 16 in 1977. Weeks hit 16 homers in 2007. ... Weeks' sixth leadoff homer tied a franchise record. ... Chipper Jones (hamstring) was in the original Braves lineup before he was scratched an hour before the game. ... The Braves are 13-1 in home day games. ... Diaz has three homers, all in the last 11 days. ... Parra also allowed 10 runs on June 2, 2009, at Florida.