Hayes had his best finish in a major championship at the U.S. Open in 1980, where he began the final round of play two shots out of the lead but shot a final round 74 to finish T6. He was also the first round leader at the 1975 PGA Championship, but finished T22. In the second round of The Open Championship in 1977, Hayes shot 63 at the Ailsa Course at Turnberry to establish a new single round record at The Open Championship by two strokes. The previous record of 65 was set by Henry Cotton in the second round in 1934 at Royal St. George's.