FARMINGDALE, N.Y. - David Duval walked off the 18th green Monday afternoon waving his white cap.

A show of surrender?

Not from Duval. Not this week, when his improbable U.S. Open quest often seemed doomed, only to see him rally every time and nearly get his name etched on the trophy.

“It may be arrogance,” Duval said, “but this is where I feel like I belong.”

Once the world’s No. 1 player and someone who entered Monday as the planet’s 882nd-best golfer — he leapfrogged 740 players by day’s end, up to No. 142 — Duval was beaten by only one player this week at Bethpage Black, finishing two shots behind Lucas Glover and in a tie for second with Phil Mickelson and Ricky Barnes.

It was his first top 10 since 2002, netting a check for $559,830 that nearly matched what he’s made in the last five years combined.

“It’s very difficult to sit here and say second place is a failure,” said Duval, who led the field with 19 birdies. “It is very much a success. It’s not quite the success I had looked forward to this week and had hoped for, and in some way expected. But success, nonetheless.”

Success borne from his resilience, which was on display throughout the season’s second major.

When Duval got to the 17th tee Monday afternoon, he was tied for the lead.

He took the circuitous route, for certain.

Duval made four bogeys in a five-hole span in the second round, atoning for each one over the next 12 holes and making up all the lost ground. In the third round, two early bogeys hurt him again, knocking him far from the first page of the leaderboard. It looked like last year’s British Open, when he was three shots back after 36 holes and shot a third-round 83.

Except this was Bethpage, not Royal Birkdale.

Duval kept it together this time.

“He’s back to Old David,” said his coach, Puggy Blackmon. “He’s very, very close to what he used to be.”

Video   U.S. Open highlights: Day 5 June 22: Watch some of the best -- and worst -- shots from the final round at Bethpage Black. NBC Sports

Duval came to Bethpage tied for third Monday morning. In a flash, he was 14th — making triple bogey at the par-3 third, after a tee ball buried against the lip of a bunker and left him with no shot, then another chip airmailed the flag and rolled off the opposite side of the green.

Duval swears he didn’t think he was out of it, even then.

“I don’t quit,” Duval said.

He’s proven that before.

Duval actually enjoys telling the story of the time he shot 84 at the Masters three years ago. His son was there that day, and someone asked Duval about withdrawing because he was about a mile from the lead. Duval never considered it, not wanting to give his son the wrong message.

So after the triple on Monday, he started fighting back again. A perfect drive split the fairway at the seventh, only to get splashed by mud from the soaked ground, and led to Duval hooking his second shot about 60 yards off-line.

He recovered from that one, too — a 60-footer for birdie on the next hole did the trick.

And when he made three straight birdies on holes 14 through 16, Duval was tied for the lead.

“I may have taken it a little bit for granted years ago,” said Duval, whose last win was the 2001 British Open, his only major title. “And having to work quite hard over the course of years ... I guess the best way to put it, maybe, is I probably had a lot more fun out there in the heat of it, especially over there on the theater of 15 through 17, 18, than I’ve had on a golf course in a long time.”

The trophy slipped away in a few fleeting moments. Duval slammed a par putt on the par-3 17th off the back of the hole, hitting it just a smidgen too hard and having it come to rest two inches outside the cup. Almost in the same instant, Glover made his only birdie of the day at the par-4 16th, a two-shot swing that wound up being the final margin.

Slideshow   It's Open season Images from the 109th U.S. Open at Bethpage Black public course in Farmingdale, N.Y. more photos

“I stand before you certainly happy with how I played, but extremely disappointed in the outcome,” Duval said. “I had no question in my mind I was going to win the golf tournament today.”

He’ll go back to the British Open in a few weeks, and he’s now assured of another trip to the Masters, where he has finished second twice.

Augusta isn’t just a perk from this week’s success.

Blackmon says it’s now Duval’s biggest goal.

“This was my comment to him a year ago: I will not go to my grave until he wins a Masters,” Blackmon said. “He plays that golf course as well as anybody.”

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