The 34-year-old Englishman will be in charge of kickstarting Europe's comeback against the United States, who currently have a 10-6 lead.
World number two Tiger Woods will be the last man out for the USA, and he will go head-to-head against Francesco Molinari.
Europe need to score eight points from the 12 singles to reach 14 points and retain the Ryder Cup.
As for the US, they need to collect four and-a-half points to win the competition.
Sunday's full draw:
Bubba Watson v Luke Donald
Webb Simpson v Ian Poulter
Keegan Bradley v Rory McIlroy
Phil Mickelson v Justin Rose
Brandt Snedeker v Paul Lawrie
Dustin Johnson v Nicolas Colsaerts
Zach Johnson v Graeme McDowell
Jim Furyk v Sergio Garcia
Jason Dufner v Peter Hanson
Matt Kuchar v Lee Westwood
Steve Stricker v Martin Kaymer
Tiger Woods v Francesco Molinari