Tied for second place were fellow Americans Kirk Triplett, Brad Faxon, Kenny Perry and Stewart Cink.
"I had mixed feelings out there because I watched him with admiration all week, " said Cink.
"He made some long putts and got it going, " US captain Pavin said of Cink's performance.
He had a 68 and tied for sixth, along with Brian Davis (67) and Stewart Cink (70).
The 2009 Open champion Stewart Cink and Matt Kuchar will form the opposition for McIlroy and McDowell.
BBC: Ryder Cup 2010: Westwood aims to lead Europe by example
Stewart Cink and Matt Kuchar were together once more and were playing with Zach Johnson and Hunter Mahan.
Cink praised the crowd at St Andrews after bowing out with a two-over 74 to finish one over par.
But thousands of hearts around the world were broken when he finally capitulated in a play-off to Stewart Cink.
Ogilvy, who was also runner up in the WGC event in 2007, proved too good for Cink in his semifinal.
Cink put it into the bunker off the tee and near the green and made his only bogey of the day.
"I didn't win any majors for about 50 starts, " said 36-year-old Cink.
Stewart Cink and Matt Kuchar lead Rory McIlroy and Graeme McDowell while Bubba Watson and Jeff Overton are up on Padraig Harrington and Luke Donald.
Since his playoff win over Tom Watson at Turnberry Cink has been hoisted into the hierarchy of players at the top of the men's game.
Defending champion Stewart Cink looks to be out of the running after a 71, although an eagle at the 18th lifted him to one under par.
World number two Phil Mickelson saw his own hopes evaporate as a dire finish dropped him to one over, while defending champion Stewart Cink finished on the same score.
Cink led the US fightback, rattling in five birdies as he and Kuchar finished the day two up against McIlroy and McDowell after 11 holes having been one down.
South African Tim Clark hit a final-hole eagle as he and Fiji's Vijay Singh defeated Lucas Glover and Stewart Cink to claw back vital points for the international team.
Cink returned from the delay by making a 5-foot par putt, an 18-foot birdie putt and a 10-foot par save on the 17th to get within two shots of the lead.
Welshman Woosnam, the 1991 champion, is off in the first group at 0800 (1300 BST), while Woods tees off alongside fellow American Stewart Cink and India's Jeev Milkha Singh at 1352 (1852 BST).
Fred Couples' men always looked set to clinch the trophy after British Open champion Stewart Cink gave them a winning 4 and 3 start against Adam Scott in the first match of the day.
McIlroy made the cut at Redstone, but three bogeys in his last six holes saw him fade to a tie for 48th after Saturday's third round -- which left him nine shots behind leaders Bill Haas and Stewart Cink.
Other pairings included Masters champion and world number two Phil Mickelson with Rickie Fowler, the youngest player in the US team at 21, Jim Furyk and Jeff Overton, Stewart Cink and Matt Kuchar and Bubba Watson and Dustin Johnson.
The focus on Watson is to take nothing away from Cink, who holed out from 15ft on the 18th to set Watson a target and then held his nerve to make his own dream come true and claim a first major title.
Cink is looking for his first victory since the 2009 British Open, but he and Haas were just one shot ahead of a group of four players -- and another nine were a stroke further back, including former major winners Louis Oosthuizen, Angel Cabrera and Keegan Bradley plus ex-world No. 1 Lee Westwood.
Australia helped the International side's cause -- antipodean Adam Scott and South Africa's Ernie Els earned a point with a two and one victory over Hunter Mahan and Sean O'Hair then Robert Allenby combined with Fiji's Vijay Singh to defeat the champion pairing of Lucas Glover and Stewart Cink (US and British Open champions respectively).
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