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 b...