With runners on first and second in the sixth inning, Kurt Suzuki hit a sharp grounder to Rodriguez, who stepped on the bag and threw to second baseman Robinson Cano. Cano's relay to first baseman Nick Johnson barely beat Suzuki.
An inning earlier, Rodriguez had engaged in a shouting match with A's starter Dallas Braden. It was not clear what they argued about.
It was the first triple play against Oakland since Kansas City did it in 1994.
The Yankees had gone 6,632 consecutive regular-season games without a triple play. Their last one came on June 3, 1968, with first baseman Mickey Mantle catching the final out on a ball hit by Minnesota's John Roseboro.
Roseboro's liner was caught by pitcher Dooley Womack, who threw to third baseman Bobby Cox. The relay then went to Mantle.
Cox was getting ready to manage the Atlanta Braves on Thursday against Philadelphia when he was told the Yankees had turned a triple play.
"They did? Well, I'll be damned," Cox said.
Cox recalled the play -- "I threw to Mantle at first ... I don't know how the guy never got back to first" -- and his claim to fame in Yankees history.
"Everything comes to an end. Somebody is always bringing that up," he said.