Woods, a 14-time major champion seeking a fourth WGC Match Play title, defeated McIlroy 2&1 in a morning knockout match only to fall 1-up to the 50th-seeded Dane, dropping the 18th hole when he missed a four-foot par putt.
Molinari, who made Ryder Cup history by winning all five of his matches at Le Golf National last autumn, had also won all five of his matches over the previous four days to reach the semi-finals.
Garcia had an 8-foot par putt on No. 7 to win the hole to square the match.
"It was an incredible experience for me to play with him and what he plays in front of every day", Bjerregaard said of playing with Woods.
Woods won back-to-back holes with birdies at the fifth and sixth as McIlroy's putting frailties began to show.
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Woods recovered well from a wayward tee shot at the 15th before driving into the lip of a bunker at 16, but McIlroy endured a worse nightmare that proved pivotal. Jordan Spieth, Dustin Johnson, Bryson DeChambeau and Sergio Garcia are some of the 64 best players in the world who join the only individual match-play event on the PGA TOUR schedule. He made 7, and Woods closed him out on the next hole.
Asked how it felt to pull off an upset victory, Woods said: 'I don't see it that way.
"It's awesome for the tournament, I think", McIlroy said.
"I'm going to have to go out there and play my own game and not really look at what he does", he explained.
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McIlroy was left to scurry to his auto in defeat, a rare low moment for him this year after a strong run of success that included a victory two weeks ago at the Players Championship. Kuchar lagged his 15-foot birdie putt to the hole and the match was conceded. "It was just one of those weird spots".
He 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 line before finding a bunker and conceding the hole.
Whatever dwindling hopes McIlroy might have had flickered out when Woods stared down a 13-foot putt, then sank it to close out McIlroy 2&1. "I tried to carry the momentum to the back nine".
In the first match play meeting between the pair, 2015 victor McIlroy missed a series of putts to the right and three-putted the 10th to go three down.
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Woods, who went 2-1 in his group, needed Wise to defeat Snedeker in order to advance; had they tied, Woods would have gone to a sudden-death playoff with Snedeker.