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.
"I wanted to keep the number of pitches a little bit lower today," Tanaka said through a translator after a 74-pitch outing. "But the result of just giving up one run I am pretty satisfied with."
Tanaka had success with a number of pitches, including a dominant splitter.
"When you get swing-and-miss stuff, and you can attack the zone with four different pitches, it's special," New York catcher Brian McCann said.
Braves first baseman Freddie Freeman left after two innings with a bruised left thumb. He took a hard-hit ball off his hand while playing defense.
"It's precautionary," Freeman said.
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.
Braves: Teheran went four innings, giving up one run, five hits and one walk while striking out five. He didn't allow a run over nine innings in his previous three starts.
"Outstanding," manager Fredi Gonzalez said. "He mixed his pitches well. He had a little jam there in the first inning with the meat of their order coming up and got out of that jam, punched out a couple guys. He did a nice job, he really did."
Yankees: Tanaka has allowed two runs and seven hits while striking out 10 over 9 1/3 innings in three spring training games.
Braves: Infielder Tyler Pastornicky (left knee surgery) had four at-bats in a minor league game and could play for Atlanta on Friday.
Gonzalez has not completely ruled out Pastornicky for opening day.
"You hate to say no," Gonzalez said. "You never know. I think the biggest thing is to make sure he's getting out of here healthy."
Shortstop Andrelton Simmons, slowed by a sore knee, was hitless in three at-bats.
Catcher Ryan Doumit left in the second with a bruised right middle finger, the result of taking Pete O'Brien's foul ball off his hand. He immediately walked to the dugout after being struck.
"It's tough," Freeman said of his teammate. "It was clean. Hopefully he's OK. He was in high spirits before he left here, so hopefully it's good news."
Infielder Brendan Ryan (lower back) could return Wednesday.
Reliever Andrew Bailey, coming back from right shoulder surgery last July, expects to increase his throwing from 90 to 120 feet in about a week. The Yankees think he might return in August or September.
McCann went 1 for 3, including a two-run double, in his first game against his former team.
"I was real excited to come to the park today," he said. "Getting to see a lot of guys I've spent a lot of years with, had special bonds with. I really enjoyed my time there."
McCann signed an $85 million, five-year contract with New York in December.
The Yankees optioned left-hander Manny Banuelos to Class-A Tampa.