Major league-leading Atlanta earned its third straight win and sixth in seven games overall.
Fried allowed three baserunners, all on singles, in his first start since May 5. He had been sidelined by a left forearm strain.
Fried (3-1), a runner-up for the National League Cy Young Award last season, struck out eight before exiting after 72 pitches. The 29-year-old left-hander retired his first 12 hitters with no hard contact.
"I felt sharper than expected," said Fried, who had four rehab starts in the minors. "I had a lot of nervous energy, just looking forward to this day for a long time."
"I really just tried to simplify it and and keep us in it as long as we can," he added. "These guys have been doing so good for so long. I just want to kind of seamlessly fit it and not try to mess anything up."
The Braves look even more imposing after Fried's velocity topped out at 97 mph.
"I honestly didn't think he'd be that sharp," Atlanta manager Brian Snitker said, "but that was pretty good and very impressive."
Cody Bellinger finished with two of Chicago's four hits. The Cubs had won three straight and 13 of 16.
"Fried was pitching like an ace," Chicago manager David Ross said. "He had real stuff, in the zone, mixing multiple pitches, kitchen sink thrown at everybody."
Fried improved to 5-0 against the Cubs for his career. He earned his first major league win at Wrigley Field on Sept. 3, 2017.
The Braves, who lead the majors with 209 home runs, went deep consecutively for the the second straight game and for the 14th time this season.
"I've never been part of an offense that can do that," Murphy said. "It feels like at any inning, any point we can explode for a whole bunch."
Brad Hand, acquired from Colorado at Tuesday's trade deadline, relieved Fried in the seventh to make his debut with the Braves. He allowed a hit in one inning.
Chicago starter Kyle Hendricks set down the first nine Atlanta batters. Hendricks (4-6) was charged with seven runs and eight hits in four innings
The Associated Press contributed to this report.