The triple play helped the Angels remain tied 6-6 going into the bottom of the ninth in an eventual 9-6 loss in 10 innings.
With runners at the corners and the infield playing shallow, Harold Ramirez hit a grounder to Luis Rengifo. The shortstop made the short toss to second baseman Brandon Drury to get Randy Arozarena and then threw to first baseman Nolan Schanuel.
Yandy Diaz was at third but did not go when the ball was hit. He waited until Drury threw to first to start home, but Schanuel made a perfect throw to catcher Logan O'Hoppe, who tagged out Diaz on his left shoulder before he could touch home.
O'Hoppe and pitcher Carlos Estevez both celebrated after the triple play was completed. It was the seventh triple play in Angels' history and the first since July 5, 1997, against Seattle.
The Angels had a chance to win it in the ninth when they had runners on first and second with one out, but Shohei Ohtani struck out and Drury grounded out to send it into extra innings.
"We certainly had our opportunities there. We just didn't push a run across," Angels manager Phil Nevin said. "A couple got away there in the ninth inning. That's what happens when games get like this."
The Associated Press contributed to this report.