Woodland's tee shot at his final hole, the par-four ninth, nestled in a divot in the fairway, but he still managed to reach the green in two to close out his round in sensational style.
Englishman Rose carded a record-equalling 65 in the first round
Woods' fifth major win at the US Masters in April has taken him to fifth in the world rankings led by Koepka, who has won four majors in less than two years.
Thomas says he is still trying to shake off the rust from a six-week layoff between the Memorial and finishing tied 12th at The Masters in April.
Woods, a former student of Haney's, backed his suspension from SiriusXM PGA Tour Radio show last week after comments about the US Women's Open field, saying the instructor had "got what he deserved."
Former world number one Woods, playing for the first time since missing the cut at the PGA Championship, made birdies at two of his three closing holes to stay under par.
It was the second win in less than a year for the 35-year-old Na, a Las Vegas resident who was born in South Korea but came to America when he was just 8 years old.
The 2014 US Open champion has been sidelined since March by a right wrist injury.
It will be Koepka's ninth week as the world's top-ranked player.
The 29-year-old American owned a seven-stroke lead over world number one Dustin Johnson and Thailand's Jazz Janewattananond, his only rivals within nine shots.
It happened at the PGA Championship after defending champion Koepka fired a five-under par 65 at Bethpage Black on Friday to seize a seven-stroke lead on 12-under 128.
Third-ranked Koepka, a runaway favourite to capture his fourth major title on Sunday, fired a five-under par 65 Friday at Bethpage Black to stand on 12-under 128.
That left third-ranked Koepka sharing the lead with England's Tommy Fleetwood, trying to become the first Englishman to win the event since Jim Barnes in 1919.
Woods, who ended an 11-year major win drought last month at Augusta National, competes for a 16th major title starting Thursday at the 101st PGA Championship at Bethpage Black.
Immesberger was a bartender at The Woods and knew the golf star personally, according to the report.