Sheets (3-0) won his third straight start, allowing one run and six hits with one walk and four strikeouts in six innings.
After missing all of last season while recovering from elbow surgery, Sheets signed the minor league deal on July 1 and had his contract purchased by the Braves on July 15.
Asked if the month has been a blur, Sheets said "Man, I'm just riding it, riding the wave.
"I mean, I'm on a very good team and the guys are doing the heavy pulling. I'm just trying to put in a little two cents myself, trying to help us out."
The Braves trail first-place Washington, which lost to Milwaukee 6-0, by four games in the NL East.
McCann has eight homers and 19 RBIs in his last 15 games since July 5 and has lifted his batting average from .225 to .242.
"I like hitting right now," McCann said. "It's been a good couple of weeks, a good month I guess. I'm just glad I'm back to where I have been my whole career. My first half was brutal. I just put it behind me. To be honest I think that was the best thing that's ever happened to me. It made me get back to the basics and doing what I've always done. It was a wakeup call, it really was."
McCann has six home runs and 16 RBIs in six games against the Phillies this season, giving him 17 homers overall.
Hamels (11-5), making his first start since signing the six-year extension on Wednesday, set a career high with six walks in his shortest start of the season. He allowed five runs, three earned, on four hits with seven strikeouts in five innings.
He said he has been through a lot this week.
"It was a long week," Hamels said. "I don't think I'll have to experience that again."
Hamels said he was affected by "one of the more humid days I've ever had to pitch.
"It was one of the few games I've had to change my jersey twice," he said. "I'm hoping I don't have to do that ever again."
Hamels said the humidity affected his grip on the ball.
"I tried to force the issue over and over and over," he said. "Every pitch I could throw today was problematic."
The Braves weren't expecting six walks from Hamels.
"We got Cole on an off night," said Chipper Jones. "I don't know that I've ever seen him walk five or six guys in a game. Very uncharacteristic but we took advantage of it."
The loss ended Philadelphia's four-game winning streak and cost the Phillies a chance to move out of last place in the NL East.
Sheets did not allow a run while winning his first two starts in his comeback with Atlanta. That streak of 12 scoreless innings ended before he recorded an out against the Phillies.
The Braves, helped by Hamels' control problems and a fielding error by third baseman Mike Fontenot, scored two unearned runs in the second. The inning could have been bigger, as Jones was picked off second base after his leadoff double.
Hamels walked Freddie Freeman, Dan Uggla and Paul Janish to load the bases with two outs. Sheets' grounder bounced under Fontenot's glove for an error, allowing Freeman to score. Michael Bourn's single to left field drove in Uggla, giving the Braves a 2-1 lead.
After Jason Heyward walked with one out in the fifth, Jones added his second double of the game. Hamels struck out Freeman before McCann's three-run homer, a high blast to center field, gave Atlanta a 5-1 lead.
Hamels' previous high was five walks, most recently on June 29, 2007, against the Mets. ... Jones moved into a second-place tie with Pete Rose for most extra-base hits by switch-hitters with 1,041, behind Eddie Murray's 1,099. ... The Phillies recalled IF Kevin Frandsen from Triple-A Lehigh Valley after placing 3B Placido Polanco on the 15-day DL with lower back inflammation. The move with Polanco is retroactive to Monday. ... The Braves signed RHP Miguel Batista, 41, who was released by the Mets, to a minor league contract. He will report to Triple-A Gwinnett. ... The Braves promoted LHP Sean Gilmartin, a 2011 first-round pick, to Gwinnett. ... Braves LHP Mike Minor will face Phillies RHP Joe Blanton as the series continues on Saturday night. The start time was changed from 4:05 p.m. to 7:10 p.m. to accommodate TV.