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Rory McIlroy, the new No. 1 player in golf, is not easily rattled.

He didn't see a scoreboard in the final round of the Honda Classic until he walked onto the eighth green, looked at the large video screen to his left and saw that Tiger Woods — who started the day nine shots behind — already was tied for fourth, four shots behind.

McIlroy buried a 10-foot putt for his first birdie of the day.

The pressure of trying to win and reach No. 1 in the world didn't really hit him until he was lining up a putt on the 13th green at PGA National, his concentration shattered by a cheer that could be heard a mile away from the 18th green. It was so loud that McIlroy not only knew what it was for — an eagle on the 18th green — but who it was for.

Tiger Woods.

"I wasn't really paying much attention until he made that eagle on 18," McIlroy said. "I heard the huge roar. And it definitely wasn't a birdie roar. That's when I knew that he probably got to 10."

That would be 10-under par for Woods, courtesy of a 62, his lowest score ever in a final round in his 15 years on tour. The birdie-eagle finish, just like the Tiger Woods of old, pulled him within one shot of the lead. McIlroy still faced the scariest stretch of golf at PGA National, with water in play on every shot over the last four holes.

What followed was a clutch performance worthy of the new No. 1.

McIlroy made an 8-foot birdie putt on the 13th to restore a two-shot cushion. Standing some 65 feet away, in grass so deep he could barely see the golf ball, he gouged out a wedge to 4 feet for a par he badly needed to keep momentum. On the two par 3s over the water, Nos. 15 and 17, he splashed out of a bunker toward the water and saved par both times.

The 22-year-old from Northern Ireland finally played it safe at the end, making par on the last hole for a 1-under 69 that was meaningful in so many ways.

It made him the 16th player to be No. 1 in the world, and the second-youngest behind Woods, who was 21 when he first reached No. 1 after the 1997 U.S. Open.

It was his fifth career win, three of those on the PGA Tour, which includes his record-setting performance last year at Congressional to win the U.S. Open, and a 62 in the final round to win at Quail Hollow.

And he won despite Woods, that red shirt brighter than it has been in two years, posting a score that McIlroy didn't think possible in such blustery conditions Sunday. Lee Westwood, whom McIlroy beat in the semifinals of the Match Play Championship a week earlier in Arizona, closed with a 63.

Even in such strong company, this day belonged to golf's new No. 1.

"It was always a dream of mine to become the world No. 1 and the best player in the world or whatever you want to call it," McIlroy said. "But I didn't know what I would be able to get here this quickly. ... Hopefully, I can hold onto it for a little longer."

However long, it sets the tone for a big year in golf — especially with the Masters a month away.

Even in defeat, Woods showed that he is hitting the ball well enough not to be counted out at any time. His 62, which featured two eagles in the final round, was nearly nine shots better than the average score Sunday.

"It feels good, because I felt like I was close," Woods said after the 28th runner-up finish of his PGA Tour career, and his best result since he was second at the 2009 Tour championship. "I've been close to shooting this score, or scores like this. And it was just a matter of time before things all fell into place."

Tom Gillis birdied the last hole for a 69 and tied Woods for second. Westwood was alone in fourth.

The 25-foot birdie putt on the 17th was a big moment for Woods. The eagle on the final moment was a shot under pressure that had not been seen in some time. With a 5-iron from 216 yards, he aimed at a tunnel beneath the grandstand and ripped it, the ball clearing a bunker and settling 8 feet away.

"It was a lot of fun out there," Graeme McDowell said. "It was just roars going up all over the golf course. For Rory to go out today with a two-shot lead and have Tiger shoot 62 on him and Westwood shoot 63, it just shows how hard it is to win golf tournaments on any tour in the world, but especially this tour.

"This golf season just got a lot more spicy."

But it starts with McIlroy, who had been building to this occasion when he would replace Luke Donald at No. 1. Since injuring himself at the PGA Championship trying to hit a 7-iron with a tree root in his way, McIlroy had finished out of the top five only once in 12 tournaments he played.

He won the Hong Kong Open, along with an unofficial event against a limited, world-class field at the Shanghai Masters. He was runner-up at the Dunhill Links in Scotland, the Korean Open, the Abu Dhabi Championship and the Match Play.

And he won the Honda Classic, finishing at 12-under 268, with two former No. 1 players making a move.

"It was a lot more meaningful," McIlroy said. "I think the way I won today was great. I missed a few greens coming in. I was able to get up-and-down. I made a couple of big par saves early, which kept my momentum. It was just one of those days. There was a 62 and a 63 out there, which is unbelievable playing.

"I just needed to focus on my game and do what I needed to do," he said. "And thankfully, that's what happened."

He hugged his father on the 18th green, posed with the crystal trophy and flashed a No. 1 sign. Before long, he was off to New York to spend a few days with his girlfriend, tennis star Caroline Wozniacki, before going to Miami for a World Golf Championship.

It will be his first tournament as No. 1, a spot that McIlroy intends to keep as long as he can.

"There's very few players as good at him at his age out there winning tournaments," three-time major champion Padraig Harrington said. "There are guys with potential, but he's already delivered. And he has a good balance in his life. He doesn't look like a guy who is going to burn out. He looks like he's going to be here for a while."