Debutant Lucas Bjerregaard carded five birdies and an eagle to end the hopes of Tiger Woods at the WGC Match Play.
Woods had beaten Rory McIlroy earlier in the day but missed a four-foot par putt as Bjerregaard won one-up.
In Sunday’s semi-finals world number 52 Bjerregaard faces Matt Kuchar, who beat Sergio Garcia two up after controversy over a putt that was not conceded.
Open champion Francesco Molinari surged to a 6&5 win over Kevin Na, who earlier ousted world number two Justin Rose.
The Italian will play Kevin Kisner, who won three holes in a row to beat Louis Oosthuizen 2&1.
Denmark’s Bjerregaard, winner of the Dunhill Links last year for his second European Tour title, birdied the first hole to take the lead against Woods, ranked 14th.
Three-time champion Woods, back at the Match Play for the first time since 2013, had three birdies in a row from the third to move two ahead, but his 27-year-old opponent twice levelled a fluctuating contest, rolling in a long eagle putt at the 16th.
“For some reason I felt less nervous that I did in the morning against Henrik Stenson, maybe because expectations were low,” Bjerregaard said after his victory.
There was controversy in the Garcia-Kuchar match as Garcia missed a short putt at the seventh. Kuchar had not officially conceded the return of barely a few inches when the Spaniard’s angry tap-in with the back of his putter stayed out, resulting in him going two down.
Asked about the incident he said: “It’s quite simple, I screwed up. I tapped it before he said anything. The only issue is Kuch had options.”
Molinari, who last year in Paris became the first European player to win all five matches at the Ryder Cup, extended his winning run in matchplay to 10 to reach the semi-finals for the first time.
Woods overcomes McIlroy in last 16
In the first match play meeting between the pair, McIlroy powered a 340-yard drive down the centre of the first fairway but Woods responded by sending his shot three yards further past.
Woods also had the better of things on the greens and made successive birdies from four feet to go two up after six.
McIlroy missed a series of putts to the right and three-putted the 10th to go three down.
But Woods three-putted the 12th and as the wind increased significantly from the north, McIlroy, who had only lost three holes in his previous three matches and never been behind, birdied the next from five feet to reduce the deficit to one.
The Northern Irishman hit a drive 395 yards at the par-five 16th but a poor shot with a wedge left him with a precarious stance and he went through the green with his third to an unplayable lie, before finding a bunker and conceding the hole.
Woods then sealed victory at the next with a 13-foot putt for a par.
F Molinari (Ita) beat Kevin Na (US) 6&5
K Kisner (US) bt L Oosthuizen (SA) 2&1
L Bjerregaard (Den) bt T Woods (US) 1up
M Kuchar (US) bt S Garcia (Spa) 2up