Simons is probably best remembered for nearly winning the U.S. Open in 1971 as an amateur. At the age of 21, he shot a third-round 65 to take a two-shot lead after 54 holes at Merion Golf Club near Philadelphia. That set up the possibility of Simons becoming the first amateur to win the event since Johnny Goodman in 1933. A stroke out of the lead on the final hole, his tee shot found the rough and he double bogeyed. Simons carded a 76 to finish tied for fifth, three shots out of the Monday playoff, won by Lee Trevino.