When Bill Haas walked down the 18th fairway at Congressional Country Club on Sunday, the applause came and he removed his cap, the respectful gesture from a man who was a routine two-putt away from winning the AT&T National. His final-round 66 served as a fine way to cap his fifth victory on the PGA Tour, and it restored order to an event that, for much of the week, featured a leader board that reduced a who’s-who of pro golf to one question: “Who’s that?”

Haas then walked off the green to a tunnel toward the scoring trailer, where he would sign his card and make his 12-under-par total of 272, and the three-shot win that came with it, official. But before he got there, the event’s host — swatting away gnats and sweating bullets in a blue blazer — intercepted him.

“Great playing, Billy,” Tiger Woods said.

“Hey, Tiger!” Haas said, a bit taken aback, and the two embraced. “Thanks, buddy. I appreciate it.”

Haas, 31, may look back on this performance as the time he looked down at his golf ball, thought about the instances when he — in his own words — “threw up all over myself,” and not only held it together, but extended his lead over runner-up Roberto Castro. On a difficult golf course in which no other player reached double digits under par at any point, Haas made one bogey all day, at the fifth, but then emerged out of what was once a five-way tie for the lead to put his name with Woods (twice), K.J. Choi and Anthony Kim as winners of this event at Congressional.

“As many times as I’ve choked and hit bad shots and been nervous and it hasn’t worked out, I was feeling all those things today,” Haas said. “And to hit good, quality golf shots down the stretch is such a good feeling. I wish I could explain it. It’s amazing.”

Woods, of course, knows that feeling — around the world, and on this very course. He had to watch this time, though, because of a strained elbow suffered in May that bothered him to the point it caused grimaces at the U.S. Open.

“Given the conditions, I kind of liked the way the golf course was set up, too,” Woods said. “I’ve played well here, and I was defending, so all-in-all it was a tough week from that standpoint.”

Even when he sits, though, this event is at some level about Woods. It helps support his foundation, and the foundation’s staff runs it. He presented the trophy, a handsome rendition of the U.S. Capitol, to Haas on the green at 18, and the gallery that remained cheered his every move.

But his appearance, too, included a walk through Congressional’s clubhouse, where members swarmed him for photos. The AT&T National will return to the Bethesda club next year, but the membership will vote this fall on whether to invoke an extension that would keep the tournament at Congressional from 2015 to ’17.

“The membership has been fantastic,” Woods said. “We’ve enjoyed our time here. And trust me: We would like to come back.”

Haas will be back in 2014, and he’ll return only with the best of memories. The day began with 19-year-old Jordan Spieth holing out from a fairway bunker at the first for eagle, then chipping in at the third to tie for the lead just as Haas, playing with Castro and James Driscoll in the final group, were reaching the first green.

“You feel the pressure,” Spieth said, “and you feel the adrenaline.”

So it was on. At one point, Haas, Castro, Spieth, Andres Romero and Jason Kokrak were all at 7 under, tied for the lead. That’s when Haas won it.

“Nine, 10, 11 was the tournament right there,” Woods said.

Start, though, at No. 8, where Haas hit a little wedge from 70 yards to 10 feet and made birdie. At the massive ninth, which played its full 636 yards Sunday — “It almost played like a par 6, a little into the wind,” Haas said — he hit his third shot to 12 feet and drained that, a birdie he called “huge.” At 10, the par 3 across water that carries a full 212 yards, he pulled out 5-iron and hit it to 10 feet, his third birdie in a row.

And at 11, Congressional’s most demanding hole, he had to deal with his memory from Saturday, when he made a triple-bogey 7 there. His solace Sunday: He had responded a day earlier with birdies on 12 and 13. “It will be fun to look at that scorecard down the road,” he said.

But Sunday, he still had work to do. Spieth, Kokrak and D.H. Lee — who posted the tournament’s best round, a 64 — had all suffered derailing birdies at 11. Haas, though, hit his 200-yard 5-iron approach to 25 feet, calmly made his two-putt, then used every inch of the hole on a 10-foot par saver at 12.

“You can’t breathe a sigh of relief yet,” he said, but Castro, who played exceptionally all week and closed with a 69, couldn’t match him through that stretch.

Now, Haas fits in well with the winners of this event. He entered the week ranked 29th in the world, and will rise further. He joins Justin Rose, Dustin Johnson and Phil Mickelson as the only players to win PGA Tour events in each of the last four years. What, though, would get him to that next step?

“I think it’s just a little bit of confidence here and there,” Woods said.

He found it Sunday, when he had it all — a win, the respect of the tournament host and the world’s No. 1 player, and the knowledge that Congressional, with its teeth showing, wasn’t too much for him to handle.