American captain Davis Love has put Woods out last in Sunday's singles, while world number one McIlroy is out third against unbeaten Keegan Bradley as Europe try to claw back their four-point deficit.
Luke Donald leads things off for Jose Maria Olazabal's side and will play Masters champion Bubba Watson.
Saturday hero Ian Poulter, who like Bradley has won his first three games, follows against US Open champion Webb Simpson.
Woods faces Francesco Molinari just as he did at Celtic Manor two years ago. The Italian lost 4&3.
Olazabal said: "Obviously we could not hide anything. We are trailing by four points and we have to put the players that are playing well up there.
"We knew they (the Americans) would know that but if we want to win this match at the end of the day we have to take the big guys down.
"I believe that it's not over. That's what I learned from Seve and what I tried to pass to the players. It's not over until it's over."