US Open quest begins
Thorbjorn Olesen of Denmark poses with the Italian Open trophy after victory in the competition during the final round of the Italian Open at Gardagolf Country Club on June 3, 2018 in Brescia, Italy.  Photo by Andrew Redington/Getty Images

Thorbjorn Olesen of Denmark poses with the Italian Open trophy after victory in the competition during the final round of the Italian Open at Gardagolf Country Club on June 3, 2018 in Brescia, Italy.  Photo by Andrew Redington/Getty Images

Former US Open winners Graeme McDowell, Tiger Woods and Rory McIlroy will head to Shinnecock Hills with hopes in their hearts — and some demons to overcome.

While Woods had a poor week on the greens, closing with a final round 72 to share of 23rd in the Memorial Tournament, six shots behind playoff winner Bryson DeChambeau, he was first for strokes gained from tee to green and clearly hitting the ball well enough to win another major if he can regain some confidence with the blade.

“This week I didn’t really have, didn’t feel comfortable with my lines and my feel was a little bit off. Consequently, I missed a bunch of putts,” Woods said. “If I just putt normally, I probably would be right there with those guys and up there in the last couple of groups."

McIlroy will worry about the swing gremlins that crept in as he slipped to a 74 on Friday to scrape through the cut on the mark.

But he shot weekend rounds of 64 and 69 at Muirfield Village to sneak into a tie for eighth on 11-under par,  just four shots behind DeChambeau, Kyle Stanley and Ben An.

The Korean set the clubhouse target at 15-under with a closing 69 and looked on as joint leaders DeChambeau (71) and Stanley (70) both bogeyed the 18th to send the event to a sudden-death playoff.

Stanley bowed out with a bogey at the first extra hole and it was DeChambeau (24) made up for his three-putt on the 72nd hole by slotting a 10-footer for a winning birdie on the second extra hole for his second PGA Tour victory.

"I can't even describe it right now," DeChambeau said. "Just to be able to win [Jack Nicklaus'] event is such an honour. He's the greatest to play. To be able to do that, I am speechless honestly."

He was even asked if, deep down, he was hoping to see a Woods' charge so he could have the chance to hold off the 14-time major winner.

"No," he said with a laugh. "He's Tiger Woods!"

On the shores of Lake Garda, McDowell recorded his best finish since he was fourth in the British Masters 18 months ago when he tied for fifth behind Thorbjorn Olesen in the $7 million Italian Open.

The Dane denied a charging Francesco Molinari a third title on home soil when he made a clutch eight-foot par putt on the final green to win by a stroke on 22-under par.

The pair traded blows all afternoon with the Italian, who was seeking back-to-back wins after his triumph in the BMW PGA at Wentworth, holing a 30 footer for birdie at the 18th to set the clubhouse target with a six-under 65.

But Olesen kept his nerve, holing out for a seven-under 64, his fifth European Tour title and a cheque for just over €1 million.

McDowell's biggest handicap heading to the US Open is that he has not won for two and a half years and his lack of recent experience in final groups on Sunday.

But while he admitted he was too protective in the third round and blew himself out of the tournament with a level par 71, his seven-under 64 yesterday, coupled with his 12th place finish at Wentworth, is a major boost.

"Saturday was disappointing, with a level par in easy conditions, being in that last group I think maybe had that sort of protecting mentality a little bit, when deep down, I knew we had to keep the accelerator down," he said.

"But we all got off to slow starts and I missed a couple short ones coming in last night but great to bounce back today and play as well as I did."

With the Ryder Cup vice-captaincy easing the pressure on his shoulders, he believes he can still push for a fifth appearance as a player and a big performance at Shinnecock Hills would be no surprise given his experience.

“Always nice to go low on Sundays, and that's the X-factor that's been missing in my game a little bit the last few years really,” the 2010 US Open champion said. 

“Days like today are really important. Really pours a lot of confidence and belief back into the game.

"As someone said earlier, since I got announced as vice-captain, I've never looked more likely to be on the team than I have the last two weeks. 

"It's ironic, but listen, being a player on the Ryder Cup Team in France this year is still a huge goal of mine this summer and I think it's achievable, still. 

"It's going to require a lot of great golf. There's a lot of great players ahead of me. But if I can play pressure-free golf and enjoy my golf the way I have the last few weeks, I think I can give it a run."

Paul Dunne made eight birdies in a 68 to finish tied for 30th on 11-under,  one stroke ahead of Pádraig Harrington, who also shot three-under yesterday to finish tied 36th.

Harrington and Shane Lowry will join Seamus Power in the FedEx St Jude Classic in Memphis this week but like Dunne, they have 36-hole US Open Sectional Qualifying today with the top 60 in the world rankings next Monday, June 11, also getting to Shinnecock Hills.

Dunne and Harrington go at Walton Heath, where they will be joined by Gavin Moynihan and his clubmate from The Island, Paul McBride, who is making his professional debut.

Lowry, who closed with a two under 70 in the Memorial Tournament to finish tied 52nd on three under, will tee it up at Brookside Country Club and Lakes Country Club in Columbus with Power going for his spot at Ridgeway Country Club and Colonial Country Club's South Course in  Memphis.

Meanwhile on the Challenge Tour Derry's Ruaidhri McGee shot a pair of six-under 65s at the weekend to tie for fourth in the Swiss Challenge in Lucerne, eight strokes behind wire-to-wire winner Marcel Schneider on 14-under par.

The German (28) closed with a four-under 67 to win by six strokes with Tullamore's Stuart Grehan tied for 33rd on seven-under after a following Saturday's 64 with a 74 and Ardglass' Cormac Sharvin 63rd on one-under after a 70.

Former Ryder Cup captain Paul McGinley tied for fourth in the Staysure Tour’s Shipco Masters in Denmark, four shots behind winner Colin Montgomerie on seven-under-par.

The Scot closed with a five-under 67 to win by three shots on 11-under par from Paul Eales and Barry Lane as Des Smyth (74) tied for 17th on two-under.

Headfort’s Brendan McGovern was tied 44th after an 81 featuring a sextuple bogey nine at the tough, 200-yard par-three fifth with Philip Walton 53rd after a 77 at Simon’s Golf Club.