The Phillies won two of three from the Braves after opening the season with a 1-5 homestand.
"It feels good to win two in a row," said Phillies shortstop Jimmy Rollins, who led off the game with a homer. "That's something new around here. That's just the beginning."
Utley was hitting only .200 with no homers while Floyd (1-1) had an ugly 10.13 ERA after his first start.
For Floyd, the key was to attack.
"It feels better to be able to let loose and let it go," Floyd said. "That's what I focused on. ... The whole thinking process of being perfect or whatever just went out the window."
Floyd gave up five hits and left the game with a 6-3 lead.
Tom Gordon earned his second save by stranding two runners in the ninth.
"I was leaving balls up and they hit them out of the ball park," Davies said.
Utley added another home run in the fifth inning to chase Davies (0-1). The Phillies second baseman added a sacrifice fly in the seventh off reliever Lance Cormier, giving him four RBI for the game.
"He has been trying a little bit too hard," Philadelphia manager Charlie Manuel said of Utley. "He gets in a little funk, but he'll bust it and come out of it. He's fine. I don't worry about him."
Utley, who hit 28 homers and drove in 105 runs in his first full season in 2005, had no homers and three RBI through his first 30 at-bats this season.
Francoeur, last year's rookie sensation for Atlanta, was also struggling, coming into the game with an .081 batting average.
"I gotta say it just felt good to hit a ball solidly," Francoeur said. "I just felt comfortable tonight. Just letting it kind of work its way out, seeing it and swinging at it."
The Phillies took their third straight series win at Turner Field. The Phillies have won five of the last nine series against the Braves in Atlanta.
The Phillies came to Atlanta with a 1-5 record.
Davies threw 31 pitches before recording his first out, a groundout by Ryan Howard that drew a sarcastic cheer from Braves fans.
"He was just a little too geared up in the first inning," said Braves manager Bobby Cox of Davies. "But after that he spotted the ball well, changed speeds.
"You gotta remember you've got to pitch in the first inning, not just throw."
Before the first out, the Phillies pounded Davies for five hits and five runs. Rollins led off with a homer. After a double by Aaron Rowand, Abreu followed with a two-run homer to left. Utley's two-run homer to center drove in Pat Burrell for a 5-0 lead.
Davies needed 40 pitches to get out of the first inning and had thrown 84 through four innings. He gave up nine hits and six runs in 4 2/3 innings as his ERA climbed to 8.38.
The Braves tried to rally, scoring runs in the first, second and fourth innings.
Renteria, who reached on a single, scored on Andruw Jones' sacrifice fly in the first inning. Francoeur's first homer cut the lead to 5-2 in the second inning. Adam LaRoche led off the fourth with a double and scored on a sacrifice fly by Brian McCann, trimming the lead to 5-3.
Utley, who carried a 1-for-19 slump into the game, gave Philadelphia a 6-3 lead with his second home run.
Through 10 games, the Braves' five starting pitchers are 0-5. The last time the Braves had no starting pitcher with a win after 10 games was 1988.
- The Phillies sent nine batters to the plate in the first, the second time in two nights they batted around in an inning. They sent 10 to the plate while scoring four runs in the second inning of a 7-5 win Wednesday night.
- Rollins' first-inning homer was his 14th career leadoff homer, tying him with Juan Samuel for the Phillies' record.
- Davies gave up four homers for the first time in his career.