The veteran right-hander Blanton blanked the Braves on three hits, while two late homers from Laynce Nix and Shane Victorino broke the game open.
It wasn't the way the Braves wanted to end the homestand on the eve of a tough nine-game road trip with series against the Rockies, Cubs and Cardinals. In fact, it was a major letdown from the high of the previous night.
"But we've played pretty well on the road," Braves second baseman Dan Uggla said.
The Braves are 8-5 at home and 7-6 away from Atlanta after falling to 3-4 on the homestand by dropping two of three against the Phillies.
After getting 19 hits the night before in the dramatic walk-off victory in 11 innings, the Braves could do little with Blanton, who tossed the third shutout of his career and first since 2007.
Blanton (3-3) threw just 88 pitches and faced only two batters over the minimum.
"He pitched as well as I've ever seen him," Uggla said. "We couldn't get anything going."
Delgado was nearly as good, allowing two runs on six hits in eight innings. He struck out five and walked none while throwing 110 pitches in the longest outing of his 12-start career that featured seven appearances last season.
"He knew exactly what he had to do and he did it," Gonzalez said, noting Atlanta's short-handed bullpen.
The game didn't begin well for Delgado, who came in with a 6.30 ERA.
Jimmy Rollins lined a leadoff single and Juan Pierre beat out a bunt. Delgado was able to limit the damage to a run on a sacrifice fly by Hunter Pence, and the young righty soon began mowing the Phillies down.
"I felt more comfortable," Delgado said.
"I'm proud of him," catcher David Ross said. "He pounded the strike zone and got ahead of the hitters, which he has had trouble doing at times."
Nix singled to open the second, but Delgado then retired 17 straight before leaving a 2-1 breaking ball over the heart of the plate. Nix didn't miss it, belting a homer over the center-field fence.
"It's a good stepping stone," Gonzalez said of Delgado's outing.
Livan Hernandez came in to pitch the ninth inning for the Braves and allowed a two-run homer to Victorino, ending any suspense.
Blanton hadn't done well against the Braves in the past, going 1-4 with a 5.19 ERA in 10 previous starts. But he baffled them this time.
After Freddie Freeman singled with two out in the first inning, Blanton didn't allow another baserunner until Ross beat out an infield hit with two out in the fifth.
The Braves' only other hit was a single by Michael Bourn with one out in the ninth. Martin Prado lined into a double play to end the game.
"You have to tip your hat to him," Gonzalez said. "But we weren't as patient as we have been."
The series finale, which lasted just two hours and two minutes, had little in common with the four-hour up-and-down slugfest on Wednesday.
The Braves' 15-13 victory on Chipper Jones' walk-off homer in the 11th won't soon be forgotten. Not only was the run total memorable, but so were the comebacks.
The Braves were behind 6-0 against Roy Halladay and 12-8 later on after battling back to take the lead. Only one other time in the past 30 years had a Major League team -- the 1995 Mariners against the Rockies -- been able to overcome deficits that large and win.
The game was also the highest-scoring extra-inning contest in the National League since the Mets outlasted the Braves, 16-13, in 19 innings on July 4, 1985.
With the comeback thriller, the Braves snapped an eight-game losing streak to the Phillies. There was no carryover, though, barely 12 hours later. Blanton saw to that.
Asked if it was one of the better games of his career, Blanton said: "Yeah, I think so. Just from the fact there were a lot of guys that pitched last night and I had to go deep. I take that as the biggest thing. Some guys got some rest today."