Tanaka, who signed a $155 million, seven-year contract in January, struck out six and walked two. The Japanese star gave up an RBI double to Tommy La Stella in the fourth.
Braves first baseman Freddie Freeman left after two innings with a bruised left thumb in a precautionary move. He took a hard-hit ball off his hand while playing defense.
Yankees center fielder Jacoby Ellsbury was scratched due to right calf tightness. General manager Brian Cashman said he thinks the injury is a minor one.
Ichiro Suzuki replaced Ellsbury at the top of the lineup and had two hits, including an RBI single, off Braves starter Julio Teheran.