And Faldo said the 42-year-old will add to his 15 major titles after four back surgeries and 10 years since his last triumph at the 2008 US Open.
The US qualifying process ended Sunday with Jordan Spieth, Bubba Watson, Rickie Fowler and Webb Simpson taking the final four available spots, a list unchanged from the points leaders entering the week.
Nervelessly, he then ripped two huge drives down the 17th and 18th holes to effectively ensure his spot in history as just the fifth player to win both the US Open and PGA Championship in the same season, all on the back of a wrist injury a year ago that threatened his career.
Woods, a 14-time major champion, is on the team as a vice-captain, a role he filled at the 2016 Ryder Cup and 2017 Presidents Cup while he was out with a potentially career-ending back injury. That gave Koepka a two-shot cushion that allowed him to coast into the finish, much the way he did at Shinnecock earlier this summer, and at Erin Hills in last year's U.S. Open.
U.S. Ryder Cup captain Jim Furyk unveiled the team's automatic qualifiers on Monday morning at Bellerive Country Club, one day after Koepka edged Woods by two strokes to win the 2018 PGA Championship at the St. Louis area course.
"Oh, God, I didn't even know if I was ever going to play golf again", Woods said in a post-round press conference.
Woods underwent spinal fusion surgery in April past year and was arrested on suspicion of driving under the influence the following month when he was found asleep at the wheel of his vehicle. "A bit of a struggle with my game today, but I hung in there".More news: Expect President Trump to Take Security Clearances Away From Former Obama Aids
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Crowds cheered the veteran through a thrilling round that saw him miss every front-nine fairway but take only 10 putts, scrambling from dirt, trees and bunkers to stay in the hunt.
"Going from that to even being able to play this year to this, it's absolutely mind blowing", Koepka said. He said an acquaintance told him of Woods: "He won't be back".
"I thought I might see a riot", wrote the fan, who posted the video to Reddit under the username carpedonnelly. "I think there's a lot of folks out there who probably think he can help us".
"To do it in this fashion, playing against Tiger and Scotty down to the wire, it's really incredible".
Cink moved to 55th in the FedExCup standings as he looks to chase his first TOUR Championship berth since 2009. "His game ... I think the word he used is 'trending.' His game is trending". I was always trailing. "I didn't know when I was going to start this year and how many tournaments I was going to play, how well I was going to play". And there are no bigger moments in golf than the Ryder Cup.