"No giving up. We knew it was going to be a battle," Conners said. "We gave them a few holes early on, did a good job of just staying with them. It feels good to get it done."
The Internationals swept Friday's foursomes matches to grab a four-point lead and they clung to the edge even though the Americans went 4-3-1 in Saturday's matches.
"Our guys battled hard. It was a tough day. I was proud of the way they hung in there," US captain Brandt Snedeker said. "Stay the course. It's going to be a long hard day tomorrow."
Internationals captain Geoff Ogilvy of Australia was overjoyed at the fightback foursomes split.
"Amazing. Having all red on the board, being down in every match, for the boys to come back and split points in the session was great," he said.
The Americans, who lead the all-time rivalry 13-1-1, seek an 11th consecutive victory with each side needing 15.5 points to hoist the trophy.
US President Donald Trump, who attended the Americans' Ryder Cup loss last year, is expected to watch Sunday at the suburban Chicago layout, where Europe rallied for an epic 2012 "Miracle at Medinah" Ryder Cup victory over the Americans.
The Internationals, who took their only victory in 1998 at Australia, had been heavy underdogs with the US team boasting eight of the world's 11 top-ranked golfers.
Lee and Fox took three of the last four holes to win. Lee made a 23-foot birdie putt at the par-three seventh to equalize and the global side never trailed again.
"We turned it around, which was awesome," Lee said.
Conners and Taylor sparkled late as Henley and Bridgeman stumbled.
Taylor's five-foot par putt won the 11th and his 11-footer took the 12th before US bogeys at 14 and 15 gave the Canadians their first lead, setting up Conners' winning six-foot par putt at 18.