The Braves reduced their magic number to eight. They have a 9 1/2-game lead over Washington with 15 left.
Keuchel (8-5) gave up one run and three hits to win his fifth straight start.
Despite a suspect rotation, the Phillies didn't pursue Keuchel in free agency while he sat for several months. The 2015 AL Cy Young Award winner eventually signed a one-year, $13 million deal with Atlanta in June.
"I think a lot of those guys over there in the front office are second-guessing themselves and I would, too," Keuchel said.
Keuchel lowered his ERA to 3.35 and the Braves are 10-6 in his starts.
"The guy competes," Braves manager Brian Snitker said. "He leaves it out there every time he pitches. I mean, he gives everything he has out there."
Melancon got some defensive help to close it. With two runners on and one out, shortstop Dansby Swanson made a leaping catch on pinch-hitter Brad Miller's liner up the middle. Third baseman Josh Donaldson then reached over the dugout railing and snared Maikel Franco's foul pop.
Phillies starter Zach Eflin (8-12) allowed three unearned runs and three hits in 3 2/3 innings.
"He had a difficult time putting hitters away," manager Gabe Kapler said. "He didn't get one pitch up enough and Flowers punished it."
Donaldson reached on shortstop Jean Segura's throwing error with one out in the fourth and Matt Joyce followed with a single. After pinch-hitter Rafael Ortega struck out, Flowers drove a 2-2 fastball into the left-field seats to give the Braves a 3-0 lead.
The Phillies had the bases loaded with one out in the fifth, but Harper grounded into a double play.
"I have to get the job done there," Harper said.
Harper saved a run in the ninth when he made a perfect, no-hop throw to the plate to retire Austin Riley trying to score from second on a single by Ozzie Albies. He has 12 outfield assists, one shy of his career-best.
The Braves are 19-4 since Aug. 17 and 44-28 on the road this season. Their .611 road winning percentage is tops in the National League.
Braves: LF Johan Camargo left the game after fouling a ball off his right leg below the knee in the fourth inning. Snitker said he's day-to-day with a contusion. ... RF Nick Markakis took live batting practice and threw from the outfield. He'll do it again Thursday. He could return this weekend against the Nationals.
Phillies: LF Corey Dickerson left the game with left foot soreness after grounding out in the sixth. X-rays were negative. ... RHP Edubray Ramos threw 15 pitches in a live batting practice session. It's still uncertain when Ramos could return to the bullpen.
More AP MLB: https://apnews.com/MLB and https://twitter.com/AP-Sports
Yankees GM rappels building, gets fan's message on Gerrit Cole
Brian Cashman saw a message taped to a 10th-floor window while prepping for a festival in Connecticut. "Please sign Gerrit Cole," it said. The GM's response: "I'm open to do clearly whatever, as always, is important for the Yankees."
Rays' Blake Snell strongly reacts to Tommy Pham trade on Twitch
Rays pitcher Blake Snell acknowledged that he overreacted -- in a moment captured on Twitch and shared on social media -- to news that teammate Tommy Pham had been traded to San Diego.
What's next for the teams that lose the Gerrit Cole sweepstakes?
One team will land the best pitcher on the planet. The rest of his suitors? They'll have to scramble.
Source: Nationals agree to deal with World Series hero Howie Kendrick
Howie Kendrick, who capped the Nationals' improbable run to their first World Series title last season with a Game 7 home run, has reached an agreement on a one-year, $6.25 million deal to return to Washington, a source told ESPN's Jeff Passan on Friday.
Win-now Padres pay steep price for Tommy Pham
San Diego took another step toward contending in 2020 by adding the outfielder but shipped one of its best prospects to Tampa Bay in the process.
Nationals owner Mark Lerner says team can't keep both Stephen Strasburg and Anthony Rendon
Stephen Strasburg and Anthony Rendon were key components in the Nationals winning the franchise's first World Series title this year, but Mark Lerner, the team's principal owner, is already preparing to say goodbye to at least one of them in free agency.