OAKMONT, Pa. — Dustin Johnson has spent most of his career feeling as if something were hanging over his head, so the cloud of uncertainty with an air of absurdity did not faze him yesterday at the U.S. Open. After years of heartbreak and one last headache, Johnson kept playing his game and being himself, and he finally became a major champion.

From the 12th hole on, he did not know for sure what his score was because an official of the U.S. Golf Association told him that he might be retroactively assessed a one-stroke penalty. That did not stop him from showing the raw power and uncanny touch that convinced most people in the golf business that one day he would win a major title.

The 31-year-old did just that Sunday, wiping out the memory of repeated disappointments when he confidently drilled a 190-yard 6-iron shot onto the 18th green within three feet of the hole and made the birdie putt. The crowd chanted his name. Jack Nicklaus, standing greenside, congratulated him. Johnson’s son Tatum embraced him, his girlfriend Paulina Gretzky kissed him. That the USGA ultimately did tack on a penalty shot did not prevent him from hoisting the big silver trophy and winning by three shots.

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“To get it done in a major, especially since I’ve been close so many times, it’s an unbelievable feeling,” he said after he officially finished at 4-under-par through four rounds at venerable Oakmont Country Club. “It’s hard to even describe.”

It was fitting that it was not going to come easily, considering how frustratingly close he had been before. He lost a three-stroke lead in the final round of the 2010 U.S. Open. Last year, he had a putt on the final hole to win the U.S. Open, but three-putted and missed even being in a playoff. The ending of the 2010 PGA Championship was the most bizarre, when he was assessed a two-stroke penalty after his round, for grounding his club in a sand trap, and missed out on a playoff.

Nothing could have prepared him for Sunday, though. On the fifth green, Johnson saw that his ball moved while he was preparing to putt. He told a rules official that he did not cause it to move and the official agreed, meaning there was no penalty. But when Johnson reached the 12th tee, Jeff Hall, manager of competitions of the USGA, told him that other officials had watched the video and had reason to believe Johnson did cause the ball to move. Hall told him they would discuss it after the round.

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“I just told myself we’ll worry about it when we get done,” Johnson said. “There was nothing I could do about it, so I just decided to focus on the next shot and go from there. That’s what I did from there to the house. I still don’t want the penalty. But at the end of the day, it didn’t affect the outcome, so it doesn’t bother me at all.”

At the time, though, it was confusing to him and the other competitors, who were apprised of the situation. “If anything, I credit Dustin for the way he played on the way in, having that hanging over him,” said third-round leader Shane Lowry, who realized he might or might not have been tied for first on the back nine.

Lowry could not take advantage. He lost all of the four-shot lead with which he entered the final round and shot 6-over-par 76. “It was there for the taking and I didn’t take it,” the Irishman said.

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No one could overtake Johnson. And Johnson did not get in his own way this time. He left behind bad memories of a “leave” he took from the PGA Tour, which reportedly was more of a suspension amid speculation about drug use. He kept leaning on a support system that includes Austin, his brother and caddie, and Paulina’s father, Wayne, arguably the greatest hockey player in history.

On Sunday, Johnson was the greatest golfer on the planet. His “someday” finally came. He had his major moment.

“To get it done on Sunday at a major, it’s a huge monkey off my back,’’ he said. “I’ve worked so hard to get here. To get it done is definitely sweet.” About that, he was certain.