To prise the cup from Jim Furyk's hands, Europe must win 4.5 points on Sunday but a decent USA start could spice matters up.
For whatever reason, the Ryder Cup has always been a struggle for Woods.
Phil Mickelson didn't even play. Molinari doesn't normally show much emotion on the golf course but even he found himself caught up in the occasion, cupping his ear to try and raise the noise level in the crowd at one point.
It was the first time Europe had won all four foursomes matches - having suffered a 4-0 reverse in the format en route to defeat in Hazeltine two years ago - and their first sweep in either format since 1989. A third point saw Spieth and Thomas become just the fourth USA pairing to achieve that haul since it became Europe versus the US.
"I felt all along that this was a good group of guys, but I have to say, when we got here on Monday, we got together", Bjørn said.
This US team was meant to be their strongest ever, yet they were ultimately thrashed and Alex Noren provided the ideal finish for Europe - long after their victory had been secured - with a lengthy putt to beat Bryson DeChambeau on the 18th green.
- Molinari and Fleetwood got their record-breaking partnership underway with a 3 and 1 fourballs win over the misfiring Tiger Woods and Patrick Reed, but it was their crushing victory against Spieth and Thomas which really sent shockwaves through the visiting camp.More news: Meghan's mother Doria Ragland helps Duchess of Sussex launch Grenfell cookbook
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You wouldn't have known any of this was happening if you just watched Woods play this weekend, though. US captain Jim Furyk chose not to disrupt his pairings from Friday, altering only the golfers' order of play, and Team Europe continued its dominance in the early Saturday fourball matches.
However, the 42-year-old lost all three pairs matches - making it eight in a row stretching back to 2010 - and his overall record now reads 13 wins, 21 defeats and three halved matches in eight appearances, only one of which (in 1999) has produced a victory.
Only twice has a side overturned a four-point deficit on the final day although a draw would retain the trophy. The writing was on the wall for Woods, paired with Bryson DeChambeau on this occasion, after Fleetwood and Molinari opened with a birdie.
Remember when Tiger Woods was back atop the golf world after winning the Tour Championship last Sunday?
Recap: Consecutive birdies on the back nine gave Koepka the lead, but Casey fought back with a birdie on the 17th hole to earn the half-point.
Woods insisted that his body feels just fine.
"That's the frustrating thing about match play".