Tanaka (9-1) allowed one run on five hits while striking out four for the Yankees, who snapped a four-game skid.
The Japanese hurler started his June slate the way he ended May. Tanaka was named the AL Pitcher of the Month for May after going 5-1 with a 1.88 earned run average in six starts, with 42 strikeouts and six walks across 43 innings.
New York outfielder Carlos Beltran went 0-for-3 with two strikeouts in his return from the 15-day disabled list. He batted fifth as the team's designated hitter.
John Jaso hit a solo homer for the A's, who had a five-game winning streak snapped. Drew Pomeranz (5-3) gave up two runs -- one earned -- on six hits with seven strikeouts over seven innings.