Clarke and Bjorn will face Hal Sutton and Scott Verplank in the alternate-shot format. The two Americans were sidelined in the morning session.
Tiger Woods and Mark Calcavecchia will face Spains Sergio Garcia and Englands Lee Westwood in the second match. Calcavecchia also sat out in the morning, while Woods lost with Paul Azinger to Clarke and Bjorn, 1-up.
Garcia and Westwood won their morning match 4-and-3 against David Duval and Davis Love III.
Phil Mickelson and David Toms will go up against Scot Colin Montgomerie and Germanys Bernhard Langer. The European team defeated Scott Hoch and Jim Furyk 4-and-3 in four-balls.
Mickelson and Toms were the lone U.S. team to win in the morning, doing so 1-up against Padraig Harrington and Niclas Fasth.
In the final foursomes match, rookie Stewart Cink and Furyk will play the Irish team of Harrington and Paul McGinley.
McGinley and Cink both sat in the first session.
As promised, U.S. Captain Curtis Strange will play all 12 of his team members on the first day. Swedes Jesper Parnevik and Pierre Fulke, as well as Welshman Phillip Price have yet to see action.
Full coverage of the 34th Ryder Cup Matches