Like later starters Pádraig Harrington and Shane Lowry, one of them must win the $7 million event to clinch a ticket to Augusta National next week.
But while all four hope to make that trip with a win, Dunne admitted that he “can’t be thinking about the Masters” and a trip down Magnolia Lane but must concentrate instead on doing well enough on limited PGA Tour starts to earn his US card.
Ranked 78th in the world but with a chance to get his foot in the door with a big week this week, Dunne said: “It’s a quiet time on the European Tour until after the Masters and I was lucky enough to get a sponsor’s invitation last week in Puntacana and I played well and finished fifth, which got me in this week.
“That’s the reason I am over here. I’d be happy to play both tours, like everyone in the top 50 in the world you have that chance, but I have to get there first.
“You don’t get many opportunities to play over here so I have to take advantage of the chances I do get and if things work out, I will have an opportunity to win my PGA Tour card.”
The Greystones star (25) was just a shot behind the clubhouse leaders on six-under-par with four holes of his rain-delayed opening round remaining when play was suspended on Thursday night.
But he kept his hot form going yesterday morning, holing a 30 footer for a birdie two at the 16th and a 14 footer at the next to post an eight-under 64 that was good enough for a one-shot, first round lead — his first on the PGA Tour since he led The Open after 54 holes as an amateur in 2015.
The former University of Alabama, Birmingham star then carded a one-under 71 in the second round to lie two shots behind early leader Beau Hossler on nine-under par.
He must earn the same number of FedEx Cup points - 269 - to match the 150th player in last year’s FedEx Cup standings if he is to get Special Temporary Membership on the US circuit.
And he’s pleased with how things are going so far after struggling with his game earlier this year.
“I’ve been driving the ball quite well after not playing well about a month ago,” Dunne said.
“So I did some good work on my game in the weeks leading up to Puntacana and it’s been going well so far.
“It’s always hard to stop when you are playing well and come out the next morning and keep it going so to make two good birdies on the 16th and 17th this morning was very pleasing.”
Clubhouse leader Hossler opened with a 65 then added a 68 to lead by a stroke on 11-under par from Sam Ryder, who also shot four-under yesterday.
Dunne had to start his second round shortly after signing his first round card and immediately dropped a shot when he carved his tee shot into trouble and had to take a penalty drop.
He bounced back with a pitch and putt birdie four at his fourth hole but failed to get up and down from over the green at the 18th.
He didn’t lose heart, however, and hit a stunning wedge to two feet at the third to get back to eight under.
After failing to birdie the par-five fourth, he had to work hard for pars at the fifth and sixth but then chipped close to set up an easy birdie four at the eighth.
Lowry was 24th, four behind Dunne after his opening 68 but soon moved through the gears and a second successive 68 left him just three off the lead on eight-under After birdies from 12 feet at the first and five feet at the third, the Clara man made a sloppy bogey six at the eighth before surging home in 33 for his second 68 on the trot.
The world No 77 rolled in an 18 footer at the 11th, avoided a three-putt by making a six-foot return putt at the 13th before picking up shots at the next two holes.
At the par-three 14th, he hit a 218-yard tee shot to 12 feet and made the putt before getting up and down from 84 yards for his birdie at the par-five 15th.
Power and Harrington, who opened with five-under 67s to share 10th spot behind Dunne after the first round, were among the late starters last night.