DUBLIN, Ohio -- The drama was more than Jon Rahm wanted. The result was what he always imagined.

Rahm became the No. 1 player in the world Sunday with a victory in the Memorial, in which he watched an 8-shot lead at the turn shrink to three shots with three holes to play and then hit what he called the greatest shot of his life, which turned into a bogey because of a penalty.

All that mattered was the fist bump -- not handshake -- with Jack Nicklaus and taking his place along his idol, Seve Ballesteros, as the only Spaniards to reach No. 1 in the world.

With a 2-shot penalty because his ball moved the length of a dimple on his chip-in behind the 16th green, Rahm closed with 3-over 75 for a 3-shot victory over Ryan Palmer.

Rahm got up and down on the final four greens, which made it even sweeter.

"One of the best performances of my life,'' Rahm said. "Yesterday was probably one of the best rounds of my life and finished today with some clutch up-and-downs. As a Spaniard, I'm kind of glad it happened that way.''

The fiery emotion is his hallmark. He showed it on a tee shot that sailed left into a creek on the 11th hole, slamming his club into the ground in a pique of anger. It was also evident with a ferocious fist pump after his flop shot from deep rough behind the 16th green rolled into the cup.

Birdie or bogey, it was a winner, a shot that would have made Ballesteros proud.

"I still can't believe it, I'm not going to lie,'' Rahm told Nicklaus off the 18th green.

With the penalty -- Rahm had no idea it was an issue until after his round but accepted the penalty when he saw video that zoomed in on the ball -- he finished at 9-under 279 for his 10th career victory and fourth on the PGA Tour.

Muirfield Village played its toughest in 42 years, with only five players under par, the fewest for the final round since the tournament began in 1976. Rahm's 75 was the highest finish by a winner since Roger Maltbie shot 76 the inaugural year.

The rough wasn't cut all week. The greens were allowed to go to the edge because they are being replaced. Crews stripped the entire fifth green as the leaders were on the back nine.

Rahm looked to be playing a different course. He played bogey-free on the front nine, with birdies on the two par-5s. That put him eight shots clear on his way to No. 1.

Then he made bogey on the 10th. Not a problem.

He yanked his tee shot into a creek on the par-5 11th, and that was a bigger problem, based on how hard he slammed the club into the ground in a pique of anger. He made double-bogey. Palmer made birdie on the 12th, and Rahm made another bogey from the bunker on the 14th.

Just like that, the lead was three shots.

Only a week ago at Muirfield Village for the Workday Charity Open, Justin Thomas had a 3-shot lead with three holes to play and wound up losing in a playoff to Collin Morikawa.

Rahm was worried that his tee shot might find the back bunker, though the rough was not a great option with how fast the greens were running. Rahm was thinking that anything inside 10 feet would be good. This was perfect, with the ball landing on the fringe and sliding down the slope into the cup.

As for the penalty?

"It doesn't change the outcome of the tournament,'' he said. "It just puts a little bit of an asterisk in it, in the sense of I wish I could just keep that birdie because it was one of the greatest shots of my life, right?''

The chip was similar -- but from a different angle -- to Tiger Woods' chipping in from behind the 16th green when he won the Memorial for the fifth time in 2012.

Woods, in his first competition since Feb. 16 because of the COVID-19 pandemic, shot 76 and tied for 40th.

Matthew Fitzpatrick had a 68 for the low score of the final day to finish third.

The consolation prize went to Palmer (74) and Mackenzie Hughes (72), who earned spots in the U.S. Open in September at Winged Foot as the leading two players from the top 10 who were not already eligible.

Henrik Norlander could have taken the final spot with a par on the 18th, but he missed the fairway well to the right, couldn't reach the green and made bogey. Norlander and Hughes tied at 3-under 285, but the spot went to Hughes because he had the better world ranking.

That ranking now starts with Rahm, who only four years ago was at the Memorial to receive the Jack Nicklaus Award as the nation's best college player.

Now he's the best in the world, a ranking Rory McIlroy had since Feb. 9.

"He deserves it," McIlroy said after his tie for 32nd. "He's been playing great for a long time. Even the display this week, it's pretty impressive."

The Associated Press contributed to this report.