Tiger Woods' abject Ryder Cup ended with a fourth defeat from as many matches as Europe moved to the brink of glory at Le Golf National.

Trailing 10-6 overnight, the United States won three of the first four contests to finish and halved the other to close within a point of their hosts.

However, Thorbjorn Olesen produced a stunning display to thrash Jordan Spieth 5 and 4, and Thomas Bjorn's side held some healthy leads further down the draw as Rahm beat Woods 2 and 1.

Having recovered from two down to be all-square through 12, Woods - last week's Tour Championship winner - bogeyed the 13th and 14th to fall two down and could not recover, Rahm sealing victory with a sensational approach to the 17th.

Rahm's victory took Europe to 12.5 points, two short of the number they needed to regain the trophy.

Elsewhere, Henrik Stenson was four up on Bubba Watson through 11, while Francesco Molinari - seeking to become the first European to win five points from as many matches - was two up on Phil Mickelson through 13 and both Ian Poulter and Sergio Garcia were one up as their contests neared a conclusion. 

In the opening match, Justin Thomas got the better of Rory McIlroy in dramatic style at the 18th, as the Northern Irishman found a plugged lie in a fairway bunker, failed to escape the trap at the first attempt and then stuck his next shot in the water.

"It was an extremely unfitting way for that match to end," Thomas told Sky Sports. "I'm very happy to get the point for our team, but I didn't want to get it like that."

A fantastic contest between Paul Casey and Brooks Koepka finished all-square, the former making a super birdie to win the 17th before his opponent pulled off a clutch up-and-down to halve the last.

Tommy Fleetwood's magnificent Ryder Cup debut ended on a sour note as he was trounced 6 and 4 by an inspired Tony Finau, while Webb Simpson delivered a hugely impressive display to beat Justin Rose 3 and 2.