The US squad took an 11-7 lead into 12 concluding singles matches at Quail Hollow, needing four wins and a tie to capture the trophy again.
The Americans own an 11-1-1 lead in the all-time rivalry and have never lost on home soil.
But the Internationals sparked some Sunday drama by taking five of eight points on offer Saturday.
Australia's Cam Davis eagled the 16th hole and birdied the last two while 20-year-old South Korean Kim Joo-hyung birdied the 18th to each deliver emotional 1-up pairs triumphs.
"We're going to have to turn around and come out hot and try to get the momentum back," US captain Davis Love said.
Sunday's singles began with Thomas, who won the 2017 PGA Championship at Quail Hollow and his second major at this year's PGA, facing South Korean Kim Si-woo and three-time major winner Spieth meeting Davis in match two.
Thomas and Spieth became only the third pairing to finish a perfect 4-0 in foursomes (alternate shot) and four-ball (best ball) matches in a single Presidents Cup.
"We put some guys that are playing really well up front, and then we put some guys in the last four matches that we trust," Love said.
The US team, with 10 of the world's 16 top-ranked players to none for their global rivals, was a heavy favorite over an Internationals side that lost British Open champion Cam Smith and several other top players who jumped from the PGA Tour to LIV Golf, making them ineligible.
The Internationals need 8.5 points from 12 matches to stage what would be the greatest last-day comeback in Presidents Cup history and lift the trophy for the first time since 1998.
"We've got to get off to a red-hot start," Internationals captain Trevor Immelman said. "Our goal has to be to go out and make putts like this course has never ever seen before."
Love knows all-too well it's not an impossible task. He was the US captain in 2012 when Europe, trailing by four entering singles, took 8.5 points to win the Ryder Cup in the "Miracle at Medinah."
A repeat US flop on the final day a decade later would sting even deeper, given the ranking might of the Americans and the diminished state of the Internationals.
Masters winners Hideki Matsuyama of Japan and Adam Scott of Australia were set for the third and fourth matches, Matsuyama against Sam Burns and Scott meeting Patrick Cantlay.
Scott, making his 10th Presidents Cup appearance, has never played on a winning team.
"Over the course of my career in this, there haven't been many times I've felt momentum going our way," Scott said. "We certainly have it... and it will be great if we could keep it rolling."
Homa plays Kim late
Top-ranked reigning Masters champion Scottie Scheffler, winless in three starts paired with Burns, was matched against Colombia's Sebastian Munoz just ahead of Tony Finau and Canada's Taylor Pendrith in match six.
Tokyo Olympic champion Xander Schauffele faced Canada's Corey Conners with South Korean Im Sung-jae playing Cameron Young in match eight followed by South Korean Lee Kyoung-hoon up against Billy Horschel.
Kim Joo-hyung, whose fist-pumping emotional style sparked the global side, was matched late against Max Homa, who delivered a clutch 1-up win of his own with a birdie at 18.
"As far as putting him out earlier, we have our system and we try and run it," Immelman said of Kim. "And we see what happens."
The final matches had two-time major winner Collin Morikawa against Chile's Mito Pereira and Kevin Kisner against South African Christiaan Bezuidenhout.
