The South African duo turned 1-up and began to close the net early into the back nine. They went 2-up at the 11th after Reed/Kuchar conceded the hole, and then followed that with another at the 12th hole, where Oosthuizen drained a 20-foot birdie putt from the fringe.
It was steady golf from there onwards by Oosthuizen/Grace and they scored pars right the way through to the 16th, leaving Kuchar/Reed with all the work to do.
It proved to be too great a feat for the Americans, who also made pars until the match drew to a close and the International Team came away with its lone point of the Thursday foursomes.
It was fairly clinical stuff from the Americans in their other matches, with Jimmy Walker and Rickie Fowler leading the show in a 5&4 victory over Thongchai Jaidee and Anirban Lahiri.
Jason Day and Steven Bowditch managed to take Phil Mickelson and Zach Johnson all the way to the 18th, but eventually the Americans claimed the match 2-up.
New Zealander Danny Lee and Australian Marc Leishman were always going to have a tough time against Jordan Spieth and Dustin Johnson, and eventually the match went 4&3 to the gents from the other side of the Pacific.
The pairing of Adam Scott and Hideki Matsuyama looked formidable, but they lost three holes in quick succession early on Thursday and never truly recovered. They brought the match back with wins at the seventh and 10th holes, but remained 1-down to the American team of Bubba Watson and JB Holmes.
Eventually Holmes/Watson ran away with it when they made birdies at the 15th and 16th to seal a 3&2 victory.
It was a tough start for the International Team, but the Oosthuizen and Grace have provided a glimmer of hope. It will take something special to win the tournament, but at least the South Africans have proved that Americans can be beaten.