Tiger Woods believes he can claim his 80th PGA Tour win in the Honda Classic after he produced flashes of his old brilliance to lurk just four shots off the lead at halfway.

Luke List shot a four-under 66 and American compatriot Jamie Lovemark a 69 to lead by a stroke on three-under-par from Webb Simpson, Russell Henley, Rory Sabbatini and European number one Tommy Fleetwood.

But as Graeme McDowell got mangled in the Bear Trap to join Seamus Power and Pádraig Harrington in missing the cut, Woods plotted his way to a 71 to share 14th on one-over par.

"Well, I'm right there in the ballgame," Woods said after another day of attrition at PGA National's Champion Course in Palm Beach Gardens. "I feel like I'm right there. I'm right where I can win a golf tournament. 

"You know, four back on this golf course with 36 holes to go... anybody can win this golf tournament right now. It's wide open."

That includes Rory McIlroy, who is seven shots behind after he recovered from a triple bogey six at the 17th, his eighth, by relying on his putter to make the five-over par cut with a shot to spare after a second successive 72.

“Putting feels good,” said McIlroy, who made stunning birdie three at the sixth, then bogeyed the par-three seventh and had to pitch and putt for crucial pars at his last two holes. 

Insisting he's got more trust on the greens after losing it on the poa annua out west, he added: “It was nice to hole that six-footer at the last to guarantee being in for the weekend.

"I had just a little more commitment, a little more trust over the last couple days. It was nice to see a couple putts drop today."

Scores

It was more of a grind for Lowry, who was on the fringes of contention at one-over with four holes to play.

But he found the lateral water hazard twice at the sixth and followed a triple bogey seven there with a closing bogey for a 74 to sneak in for the weekend on the mark.

The Clara man must win to qualify for next week's WGC-Mexico Championship and like Woods, he's still in the ball game after another terrifying day at a course that punishes mistakes like few others.

"A little bit off and the wind is going to make it look like you're a terrible weekend golfer," defending champion Rickie Fowler said after a 76 saw him miss the cut by two.

If Woods' one-over 71 featured enough promise to convince the faithful that there are a few more glory days to come, McDowell's demise added another layer of disappointment to last Sunday's costly closing 77 at Riviera Country Club.

Level par starting the day, he was hanging on by his fingertips, four over for the day and just a shot inside the projected five over cut mark entering the feared Bear Trap.

Less than 40 minutes later he was reeling on eight-over, ricocheting off rocks into the water at the 15th before going directly into the drink at the 17th en route to a pair of costly double bogey fives.

A closing birdie four saw him sign for a 77 to miss out on seven over but as he was going through torture, Woods was creating drama of his own.

Still struggling to find fairways consistently, he followed an early bogey at the second with birdies at the fourth and ninth, revived the famous Woods' fist-pump when got up and down for par from 96 yards at the 11th, knocking in a 13 footer.

And while he found water short and double bogeyed the 15th, then three-putted the 16th from 66 feet, he raised the roof again by converting a 12-foot birdie putt at the 17th before parring the last.

Power shot 74 to miss out on 11-over with Harrington a shot further back after shooting a second successive 76 alongside McIlroy, three-putting three times and finding water twice at the sixth to run up his second double bogey of the day.

Moynihan ready to click

At the European Tour's Commercial Bank Qatar Masters, Mount Juliet's Gavin Moynihan (23) carded his lowest round since winning his card three months ago but still missed his fifth cut in as many starts this season.

Despite finishing birdie-eagle for a five-under 67, the Dubliner missed out by four strokes on level par, which was no great surprise after he had arrived in Doha just 10 hours before his first-round tee time and opened with a 77.

Darren Clarke (49) missed the cut by ten shots after a 74 but Spain's Adrian Otaegui (25) birdied the final three holes for a six-under 66 and a one-shot lead over Scotland's Stephen Gallacher, England's Eddie Pepperell, Frenchman Grégory Havret and South Africa's Erik Van Rooyen on 11-under par.

The shame for Moynihan is that he has just next week's Tshwane Open to look forward to before he takes a break until mid-April

On the Sunshine Tour, Dubliner Neil O'Briain missed the four-under-par cut in the Cape Town Open by two strokes after following an opening 68 with a 74.