Cleveland's Danny Salazar was trying to match fellow rookie Alex Wood.
The Indians struggled at the plate, however, and Salazar's night ended after 77 pitches through four innings.
"We're just in a position with him right now where, if he has long innings, we owe it to him and to the organization to keep an eye on him," Cleveland manager Terry Francona said.
"There's going to be a day when we can turn him loose and let that four turn into six or seven, but not right now."
Salazar allowed Elliot Johnson's two-run triple in the second inning as Wood joined four other Atlanta pitchers in beating the Indians 2-0 on Tuesday night.
Cleveland, despite holding the Braves to only three hits, was shut out for the eighth time this season. The Indians had won two straight and five of six.
Salazar blamed himself for shaking off Carlos Santana in the second and throwing a fastball away to Johnson when the catcher wanted something off-speed.
"I was a little bit disappointed in myself because I felt great tonight, but I couldn't find my release point," Salazar said. "Changeup, fastball, slider — everything was up."
The Braves have won two straight, improving the majors' best record to 79-52. They have won 14 of 17 at Turner Field and own baseball's home mark at 45-18.
Wood (3-2) allowed five hits, a career-high four walks and struck out five in 5 2-3 innings. He's 3-0 with a 1.46 ERA in his past six starts.
Salazar (1-2) gave up three hits, two runs and two walks in four innings. The right-hander struck out three.
Closer Craig Kimbrel pitched a perfect ninth to earn his 42nd save, most in the majors, in 45 chances.
He struck out Drew Stubbs and retired pinch-hitter Lonnie Chisenhall and Michael Bourn on groundouts.
Atlanta went up 2-0 in the second when Brian McCann walked with one out, advanced to third on Joey Terdoslavich's single to right field, and both runners scored when Johnson tripled over Drew Stubbs in front of the wall in right field.
"It hit off the wall, and he still almost caught the thing," Johnson said. "So obviously I'm glad it went our way, we got that cushion for Woody and he took it the rest of the way."
Wood issued his four walks in the first three innings, but he worked around Asdrubal Cabrera's leadoff double in the fourth and Kipnis' two-out double in the fifth.
A two-out single by Michael Brantley chased Wood in the sixth. The next Atlanta pitcher, Luis Ayala, walked Stubbs, the only batter he faced, but Scott Downs ended the threat by striking out pinch-hitter Jason Giambi.
Cabrera went 3 for 4 and was the only batter with more than one hit, but Johnson drove in the game's only runs.
Bourn, who filled the same roles for 208 games during the previous 1½ seasons with Atlanta, credited Wood with keeping Cleveland batters off balance.
"He kept attacking the zone," Bourn said after going 1 for 5 with two strikeouts. "It was our first game against him and he dominated us pretty much. But there ain't no 'pretty much' — he dominated us. We got zero runs off him. We've got to find a way to put some runs on the board and help our pitchers out."
Notes: Cleveland's bullpen has a 2.65 ERA over its past 43 games. ... Atlanta had its fewest hits in a victory since getting three on July 19, 2012, against San Francisco. ... Braves RF Jason Heyward rejoined the team for the first time since getting hit by Mets pitcher Jonathon Niese last Wednesday, breaking the right side of his jaw with a 90-mph fastball. Heyward hopes to return for the playoffs. ... Atlanta RHP Brandon Beachy was in the clubhouse one day after learning there's no structural damage in his surgically repaired elbow. Beachy, who has missed 109 games over the past two years, hopes to return by the end of next month. ... The Indians and Braves met for the first time since 2007 and for the first time at Turner Field since 2004.