And then Jaso swung at the first pitch and sent it over the right-field wall.
That was all Oakland got, though, as Tanaka tamed the highest-scoring team in the majors and the New York Yankees ended the Athletics' five-game winning streak, 2-1 Thursday.
''I know my first at-bat I hit the home run, but I actually went up there telling myself to see pitches,'' Jaso said.
''I think he was trying to get ahead, because I'm a guy that likes to take pitches and kind of work deep into the count. I think he was just trying to get strike one on me,'' he said.
Facing the A's for the first time, Tanaka (9-1) got a jolt when Jaso homered as the second batter in the game. But that was the only run the Japanese rookie allowed in six innings, and he exited with an AL-leading 2.02 ERA.
Tanaka gave up five hits, struck out four and walked one as the Yankees stopped a four-game skid. He retired 10 straight batters after Jaso's homer and left several A's taking tentative swings.
As Tanaka has demonstrated during his first 12 starts in the majors - at least six innings with three or fewer earned runs, all of them - he toughens up when there's trouble. He twice escaped two-out, two-on jams, and threw 104 pitches overall to a team known for grinding out at-bats.
Jaso had his chance in the fifth and popped up to end the inning.
After homering off Tanaka early, ''I kind of knew he was going to come with soft stuff, and he did,'' Jaso said. ''His split-finger started working for him there and he got me to pop up with runners on base.''
Before the game, A's manager Bob Melvin said there was some ''intrigue'' to seeing Tanaka up close, kidding he would've preferred Oakland miss the ace's turn.
''We made him work some, maybe a little bit more than he's had to, where his pitch count got up and they had to get him out,'' Melvin said. ''But you can see why his numbers are the way they are. He's got a lot of pitches.''
David Robertson worked the ninth for his 13th save in 15 chances, helped by a lucky bounce.
Stephen Vogt singled with one out and pinch-runner Craig Gentry stole second. Alberto Callaspo followed with a hard grounder that deflected off Robertson's leg, and first baseman Mark Teixeira corralled the carom and flipped to the pitcher covering the bag for an out. Pinch-hitter Derek Norris looked at strike three for the final out.
''I was probably the happiest guy in the stadium that the ball hit me,'' Robertson said.
Shortly after he was inserted for speed and defense, Yankees right fielder Ichiro Suzuki blunted Oakland's bid to tie it in the eighth with a sliding catch on Brandon Moss' liner into the gap with runners on first and second. After a wild pitch, Adam Warren struck out Yoenis Cespedes to end the inning.
The Yankees broke a six-game losing streak to Oakland. The A's own the top record in the AL, and best road mark in the majors.
Brett Gardner hit a leadoff homer in the third against Drew Pomeranz (5-3) for a 2-1 lead.
Pomeranz pitched a season-high seven innings and gave up six hits and one earned run.
Jacoby Ellsbury almost had a two-run homer for the Yankees in the first. He hit a drive to the top of the right-field wall, hustled around the bases and slid into second.
The umpires, however, ruled it a home run and Ellsbury got up and trotted to the plate and into the dugout. Melvin challenged the call and it was overturned to a double.
Alfonso Soriano broke an 0-for-16 slump with an RBI single in the second, set up when Brian McCann singled and continued to second as the ball skipped past Moss in left field for an error.
NOTES: The A's have homered in 13 straight games, connecting 23 times in that span. ... Tanaka had gone five starts without allowing a homer. ... Cespedes was Oakland's DH. Melvin gave the slugging OF a lighter day after hitting 2 HRs Wednesday night. Melvin also said Cespedes was working through some shoulder issue. ... RF Vogt made a nice catch in his first major league start in the outfield. He's normally a catcher. ... Seven veterans of the D-Day invasion were honored at home plate before the game.