Then for good measure, Koepka captured his third career major title on Sunday at the PGA Championship, outdueling Woods and Adam Scott down the stretch at Bellerive Country Club to shoot the lowest 72-hole score in tournament history, 16-under par 264.
But Furyk, the U.S. Ryder Cup captain, remained coy about whether he would choose Woods with one of his four at-large picks, saying Monday morning during a news conference to discuss the eight automatic qualifiers that he wanted to let the process play out until his first three picks are announced September 4.
Brooks Koepka this year achieved something only Curtis Strange and Ben Hogan have managed since the World War II and won consecutive US Opens.
Furyk will name his first three wildcards after the Dell Technologies Championship, which concludes on Monday, September 3, and he will complete his line-up with one more captain's pick the following week.
As for the Ryder Cup, Furyk ended up with the same eight players who started the week atop the US standings.
"I played hard", Woods said after finishing his final round with a six-under 64 - his best final round at a major.
"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".
Koepka also joins Woods in being one of just five players to win the US Open and PGA Championship in the same season.
"They've been unbelievable, not only supportive, but just so positive", Woods said Saturday.
"Going from that to even being able to play this year to this, it's absolutely mind blowing", Koepka said. "We will sit down and give him our input and what we think, who should be on the team".
Woods' performance at the PGA elevated him from 20th on the Ryder Cup points list to 11th. "I really look forward to it".
And the former world number one strengthened his case for inclusion in the team with a second place finish in the PGA Championship.
"I think the word he used is 'trending.' His game is trending", Furyk said with a smile.
Live coverage of Tiger Woods' battle with eventual champion Brooks Koepka drew a 6.1 rating, up 69% compared to the average household audience for the same event one year ago, according to CBS Sports.
Mickelson missed the cut at the PGA, did not contend at the British or the U.S. Open and has not been in great form since winning the WGC-Mexico in the spring.
Europe's Ryder Cup stars will hope Koepka is as accommodating when he lines up for the US team in France next month.
The tournament will take place September 6-9 at Aronimink in Newton Square, Pa., in the third leg of the FedEx Cup Playoffs. Watson and Simpson were successful together at Medinah in 2012, although neither has won a Ryder Cup singles match. Spieth and Reed have been dynamic in the Ryder Cup and Presidents Cup.
Furyk said he wasn't so sure how important the rankings were when looking to identify his captain's picks.
Furyk sounded excited about the eight who have made a team loaded with talent. "We get an opportunity to see some more guys play well".