The most notable play of Meacham's career was a bizarre baserunning gaffe which also involved Dale Berra in an 11-inning 6–5 loss to the Chicago White Sox at Yankee Stadium, on August 2, 1985. With Meacham and Berra the runners at second and first base respectively in the seventh inning of a game tied at three, Rickey Henderson hit a ball that rolled to the farthest reaches of left-center field. When Meacham slipped between second and third base, both runners ended up approaching home plate in synchronized fashion, one on the heels of the other. After catching the relay throw from shortstop Ozzie Guillén, catcher Carlton Fisk tagged out Meacham to his right, then turned to his left just a split second later to do the same to Berra, completing the double play. Yankees manager Billy Martin commented, "I've never seen that in grammar school, much less a major-league game."