Woods was making his first appearance in The Open since 2015 after returning to action in the autumn of 2017 following two years blighted by back problems and made a solid start by shooting level-par 71s in the opening two rounds.
"What's important is how well Tiger has played", Furyk said. "A bit of a struggle with my game today, but I hung in there". His game is trending. "It's a lot harder than people think".
"They bring a lot to the team room, both those players as leaders", Furyk told me.
Getting the best of Koepka sets up as a daunting challenge for Woods, though the 42-year-old, 14-time major victor could easily argue he's been through worse.
Woods was impressed with Koepka's skill.
Furyk would not be pinned down on whether Woods was guaranteed a place in the team, skirting the question, no doubt cognisant of the diplomacy his job requires.
"There's nothing like it", said Gary Woodland, who was in the twosome with the world's best-known player.
"He priceless, to be honest with you", Furyk said. "He has been a big help to our captains", Furyk said. And while he had never played Bellerive, either, links golf has a steeper learning curve than the bomb-it-and-find-it course setup in Missouri.
The last one was a laser of a 4-iron from 226m that settled 6 feet away, sending him to a dream finish of a year that began with the 28-year-old Floridian wondering if a wrist injury that kept him out four months would ever allow him to compete again.
No matter what happens over the next few weeks, Woods will be at the Ryder Cup; he was named a vice-captain last winter and Furyk said he would replace him in that role Woods is on the team. Was made a fifth vice-captain instead and made sure he would not miss out in 2018 thanks to three wins on the PGA Tour before the end of June. Watson is a two-time Masters victor.
Woods has earned five top-10 finishes in the 14 events he's played in 2018.
Seven of the Americans are in the top 14 in world rankings with Simpson the odd man out at a still-respectable 20th. Which is good news for him, as the US has not won the Ryder Cup on foreign soil since 1993.
Woods' fellow veteran Phil Mickelson is hoping for a wildcard that would give him a record 12th straight Ryder Cup appearance.
The Americans will face a different challenge from the forgiving fairways and fast greens of Hazeltine as they seek to lift the Cup on European soil for the first time in 25 years at Le Golf National just outside of Paris.
"The reason we put this system into place is to identify hot players, identify guys who are playing well right now who can help this team". "I enjoyed it way more than I probably do now playing on the tour".
Furyk was supposed to be in the media centre at Bellerive discussing the players who qualified automatically.
"I've always been, I guess, pretty cool", said Koepka, who is dating actress and model Jena Sims. As Furyk says, the door is open.
"We are looking at how our next four fit in with our eight qualifiers and how that team meshes and gels".
British Open victor Francesco Molinari of Italy and England's Justin Rose, Tyrrell Hatton and Tommy Fleetwood strengthened their hold in the European points spots at the PGA, Molinari sharing sixth and Hatton sharing 10th.