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Hubert Green began the final round with the lead, but there were 12 players within three shots. It would be 1975 U.S. Open champion Lou Graham that would make the charge, collecting birdies at 12, 14, 15, and 16 en route to a 68 and a 279 total. With four holes to play, Green needed to play even-par to win the championship. As he stepped off the 14th green, however, he was approached by tournament officials and a lieutenant with the Tulsa police, who told him that they received a phone call threatening to assassinate Green while he played the 15th. Green decided to play on and finished the tournament with police around him. He proceeded to hit his next drive into a tree, which probably saved it from going out of bounds. He managed to hit his approach to 35-feet and two-putt for par without incident. He then birdied the 16th and took a two-stroke lead to the 18th. Although he struggled on the hole, he managed to make a 4-footer for bogey and hold on to an one-stroke victory.
This year marked the final U.S. Open appearance by Sam Snead, two-time champion Julius Boros, and Tommy Bolt, who had won the 1958 Open at Southern Hills. All three received exemptions by the USGA, and all three missed the cut. This was the first time that the television broadcast of the tournament covered all 18 holes of the final round.<ref.U.S. Open coverage to include all 18 holes</ref>