Ricky Castillo won again, too, and the Americans took five of the 10 afternoon singles matches and tied another Sunday at Seminole Golf Club for a 14-12 victory.
The Americans won for the third straight time to take a 38-9-1 lead in the biennial event first played in 1922.
Nathaniel Crosby, the son of late singer Bing Crosby, became the first U.S. captain with back-to-back victories since Buddy Marucci in 2007 and 2009.
Eckroat overwhelmed Mark Power 7 and 6 in the opening match, and Coody beat Alex Fitzpatrick 3 and 1 in the second. Castillo topped John Murphy 2 and 1 to become the only player to finish the two-day event 4-0.
Hammer beat Ben Schmidt 4 and 3 in the second-to-last match, and Hagestad put the Americans over the top when he was 4 up with four to play in a 4-and-2 victory over Ben Jones.
Quade Cummins gave the U.S. a half-point, winning the 18th with a par to pull even with Barclay Brown.
British Amateur champion Long, Matty Lamb, Angus Flanagan and Jack Dyer won matches for GB&I. Long beat John Pak 1 up, Lamb topped Davis Thompson 2 up, Flanagan beat William Mouw 1 up, and Dyer edged U.S. Amateur champion Tyler Strafaci 1 up.
Long played Sunday afternoon after missing the first three sessions because of a stomach virus that affected both teams and their captains. Strafaci sat out Saturday.
GB&I took 2 1/2 of the four points in the morning foursomes to pull within a half-point.
Power and Murphy beat Coody and Pak 1 up, Lamb and Dyer routed Hagestad and Strafaci 6 and 5, and Flanagan and Schmidt halved with Hammer and Thompson. Ricky Castillo and Mouw topped Fitzpatrick and Brown 1 up.
GB&I last won on American soil in 2001 at Ocean Forest in St. Simons Island, Georgia.
The 2023 event is set for the Old Course at St. Andrews.