37th Ryder Cup - USA v Europe
Venue: Valhalla, Kentucky Date: 19-21 September Coverage: Daily highlights on BBC TV and BBC Sport website, Live on BBC Radio 5 Live and Sky Sports and updates/commentary on Red Button and BBC Sport website
Faldo has been criticised for his decision-making throughout
European captain Nick Faldo has saved Ryder Cup veterans Lee Westwood and Padraig Harrington until last in Sunday's singles showdown at Valhalla.
Westwood faces former Open champion Ben Curtis in the penultimate match, while three-time major winner Harrington faces Chad Campbell at 1904 BST.
Spain's Sergio Garcia plays rising star Anthony Kim in the first match at 1703.
Europe trail the United States 9-7 going into the 12 singles matches, but only need a draw to retain the Cup.
Faldo has taken a gamble with his order because the final two matches could prove to be irrelevant if the hosts have already reached the 14½ points they need for outright victory.
He said: "We know and believe we have a great opportunity."
In addition, Ian Poulter, who has won three points so far, has been kept back until match 10, while Graeme McDowell, who has also been impressive, will play in match nine.
I'm just really happy we are in this position but if you look at their team they are probably favourites
United States skipper Paul Azinger has packed most of his form players into the early matches, with the unbeaten Justin Leonard playing Sweden's Robert Karlsson in match three and world number two Phil Mickelson playing England's Justin Rose in match four.
Faldo revealed he had consulted his players to ask them what position they would prefer to play.
"It was a group effort, it's all about being comfortable. We want guys to play where they want to play and they can set their mind on it. I don't know if this has a theme to it," he said.
"We've been in there for half an hour doing this, everyone was involved, we thought long and hard. It's been an extremely tight match so far. Padraig wanted to go last."
Azinger said he wanted his form players to go out first.
"There was a little bit of discussion about it, I had this in my mind of how I wanted to do it and got a little bit of confirmation.
"I think it's three guys who are very aggressive, the kind I want to go first.
"Everything is so far so good but there's a lot up for grabs. We are not there yet.
"I'm just really happy we are in this position but if you look at their team they are probably favourites."
It is the first time that Europe have been behind going into the singles since Oakhill in 1995, when Faldo himself secured a vital point against Curtis Strange after coming back from one down with two to play.
Draw for Sunday's Ryder Cup singles (US players first):
1703 Anthony Kim v Sergio Garcia
1714 Hunter Mahan v Paul Casey
1725 Justin Leonard v Robert Karlsson
1736 Phil Mickelson v Justin Rose
1747 Kenny Perry v Henrik Stenson
1758 Boo Weekley v Oliver Wilson
1809 JB Holmes v Soren Hansen
1820 Jim Furyk v Miguel Angel Jimenez
1831 Stewart Cink v Graeme McDowell
1842 Steve Stricker v Ian Poulter
1853 Ben Curtis v Lee Westwood
1904 Chad Campbell v Padraig Harrington