"It was my turn tonight, but everyone else has been stepping up as well," Mesoraco said.
The victory, coupled with the Cardinals' loss to the Phillies, put the Reds in first place in the National League Central by a half-game.
During the six-game winning streak, the Reds rotation has delivered six consecutive quality starts while going 4-0 with a 2.41 ERA.
"I think it's very much expected out of us," said Bailey, who gave up two runs on four hits with one walk and six strikeouts. "I think we demand it out of ourselves more than anybody. To see Mike [Leake], Mat [Latos], Bronson [Arroyo] and all of us going out there and getting the job done, day after day, it's something we push each other for. We expect stuff like that."
Backing up the pitching during the series were 10 home runs, with 14 of the Reds' 16 runs against Atlanta scoring via the homer.
"We weren't hitting homers before, at all," Reds manager Dusty Baker said. "They come in bunches. Maybe guys are finding their stroke, their timing and their confidence. It's right on time."
That has offset other deficiencies offensively. During the winning streak, the Reds are 7-for-44 (.159) with runners in scoring position. Two of their best hitters, Joey Votto and Jay Bruce, have gone a combined 5-for-40 (.125), while the rest of the club has picked them up.
In Wednesday's 2-1 win, the Reds were 0-for-8 with runners in scoring position, but still got a walk-off homer from Todd Frazier.
"It's been a lot of the young guys coming through, which is what you like," Baker said. "It builds their confidence. They feel they belong here and worked hard to get here. "
The Reds were down by a 2-1 score on Thursday against Braves starter Randall Delgado when Brandon Phillips drew a leadoff walk in the sixth inning. A one-out single by Chris Heisey and a walk to Frazier finished Delgado's outing, as Mesoraco came to the plate against reliever Kris Medlen.
On a 2-1 offering, Mesoraco lifted it high and inside the left-field pole for the first grand slam of his career.
"It stayed true and really didn't hook at all," Mesoraco said. "It's a pretty good sign for me as a hitter. That's something I definitely look at. If you're coming around the ball, those are the ones that are going to hook foul, but that was a good swing."
"I had to go at him and you see what happens," Medlen said. "You feel bad for Randall because you hate to go in there and give up somebody else's runs, especially with the bases loaded, but I fell behind and had to go after him. We don't blame the park for anything."
The slam made a winner out of Bailey, who made only two mistakes the entire night. Both came with two outs in the fifth, while holding a 1-0 lead.
The first was allowing a single to Delgado, the pitcher. Then a 2-2 pitch to Michael Bourn was crushed for a two-run homer to right field that put Atlanta ahead, 2-1.
"I didn't really feel good tonight," Bailey said. "We just had to go out there and make do with what we had."
Bailey, who is 3-3 with a 4.19 ERA this season, has seven quality starts in his nine games.
"It's been really fun to watch Homer progress and get better and better as the year is going," Mesoraco said. "For me, there is still room in there where he can be even better.
"The thing for him that's coming along is he's throwing everything for strikes. His slider is for strikes. His curveball is for strikes. His split is a good chase pitch. He's always had the fastball, where he can put where he wants. Now with those other pitches, you can't just sit there and get yourself in a good count and wait on a fastball."
Reds reliever Sam LeCure gave up a two-out solo homer in the seventh to Juan Francisco, but Drew Stubbs got the run back with his own solo shot to left field in the bottom half that made it a 6-3 game.
Sean Marshall gave the Reds a scoreless top of the eighth and Logan Ondrusek handled the closer's role for the night. Ondrusek gave up two hits, but got a game-ending double play and notched his second save.
The Reds remain on a roll as they keep putting distance from the .500 mark at 25-19. They haven't swept a four-game series from the Braves since April 13-16, 1990, at Fulton County Stadium.
"That was a heck of a series by us," Baker said. "I can't ever recall being on a team that beat the Braves four games in a four-game series. It's a very difficult thing to do to sweep a four-game series against a quality team like that, against anybody."