Lucas Bjerregaard and Francesco Molinari will fly the flag for Europe in the semi-finals of the WGC-Dell Technologies Match Play after they recorded remarkable victories in Austin on Saturday.
Tournament debutant Bjerregaard produced a sensational finish to his last eight clash with 14 time Major Champion Woods to earn a 1up win, having earlier beaten Henrik Stenson 3&2 on a brilliant day for the 50th seed.
Meanwhile, Molinari's love affair with the format continued in the quarter-finals as he extended his winning run to ten matches with a 6&5 victory over Kevin Na.
Dane Bjerregaard will come up against Matt Kuchar in Sunday's semis after the American won 2up against Sergio Garcia, while Race to Dubai champion Molinari will face Kevin Kisner, who was a 2&1 winner against Louis Oosthuizen in a keenly fought match.
Bjerregaard made the perfect start to his crunch match with Woods, holing from four feet at the first to take a one hole lead at the earliest opportunity.
A hat-trick of wins from the third handed Woods a two hole advantage but Bjerregaard cut the gap to one thanks to a par at the short seventh.
The 27-year-old hauled himself level with a birdie on the tenth, only for Woods to win the next to regain the lead.
Woods remained in front until the 16th when Bjerregaard made a magnificent eagle from 30 feet to square the match.
The 17th was halved in birdie twos after Bjerregaard drained his 13 foot pressure putt and Woods tapped in from six feet.
And a par on the last was good enough to send Bjerregaard into the final four as Woods missed his par putt.
Bjerregaard said: "It's been a pretty incredible day. It's been emotional, that's for sure.
"I can't really explain why but I felt more nervous in the morning match against Henrik. Maybe just because there's so many people and I'm feeling a bit tired. I don't really know.
"I actually felt all right. And it was just an incredible experience for me to play with him and see what he plays in front of every day."
Molinari has not reached the final hole in any of his victories this week and only needed 13 to see off American Na.
Just as he did against Paul Casey in his comfortable last 16 win, Molinari lost the opening hole of his quarter-final contest with Na but he hit back in emphatic style, winning the next six to open up a five hole lead.
Both players found greenside bunkers at the eighth for their first halved hole of the match and the World Number Seven remained five holes up until he rolled in a superb 24 foot birdie putt at the 11th after Na had found the water with his tee shot.
Molinari had the chance to wrap up victory at the 12th but pushed his birdie try left of the hole. He did, however, seal a comprehensive win at the next when he reeled off his sixth birdie of the match.
Speaking after his win, the Open Championship winner said: "I think it's really important at this level, even if you're three or four up early, to keep going because matches can turn very easily.
"I did that very well and I'm very happy with my performance."