After Woods two-putted for par on the 16th hole to go 1-up on Sterne, the duo matched two-putt pars on No. 17 before Sterne's long birdie try came up short on 18.
Woods, meanwhile, put a 35- footer close enough in enough to tap in, prompting a concession from Sterne and the international squad for the victory at Muirfield Village.
In the day's other singles matches, Jason Day defeated Brandt Snedeker 6 & 4, Hunter Mahan bested Hideki Matsuyama 3 & 2, Jason Dufner breezed to a 4 & 3 win over Brendon de Jonge, Graham DeLaet downed Jordan Spieth 1-up and Zach Johnson was conceded a 4 & 2 win by Branden Grace.
Meanwhile, Ernie Els edged Steve Stricker 1-up, Adam Scott downed Bill Haas, Marc Leishman nosed out Matt Kuchar 1-up, Charl Schwartzel defeated Keegan Bradley 2 & 1, Webb Simpson halved with Louis Oosthuizen and Angel Cabrera got past Phil Mickelson 1-up.