The International team won Saturday’s fourballs 3-1 but still trail the United States 11-7 at the Presidents Cup heading into Sunday’s 12 singles.
The alternate shot foursomes were drawn 2-2 before Jordan Spieth and Justin Thomas put the hosts 11-4 up with their fourth point from four matches.
But Sungjae Im and Sebastian Munoz, Si Woo Kim and Tom Kim and Adam Scott and Cam Davis each won their fourballs to give the International team hope.
The winning target is 15½ points.
The 14th staging of the biennial Ryder Cup-style match is taking place at Quail Hollow, North Carolina and the US, who have never been beaten on home soil, lead the overall series 11-1 with one match tied.
Spieth and Thomas have proved the US’ most formidable pairing and followed their 4&3 foursomes victory over South Korea’s Im and Canadian Corey Conners with another comfortable victory in the fourballs, seeing off Japan’s Hideki Matsuyama and Canada’s Taylor Pendrith by the same score.
Im was paired with Colombia’s Munoz for the fourballs and they were never behind against Tony Finau and Kevin Kisner, wrapping up a 3&2 victory.
South Korea’s 20-year-old Tom Kim, playing with compatriot Si Woo Kim, then wildly celebrated after dramatically holing a 10-foot birdie putt on the 18th to earn a narrow win over Patrick Cantlay and Xander Schauffele.
Cam Davis also birdied on the 18th to secure another point for the International team alongside fellow Australian Adam Scott as they beat Billy Horschel and Sam Burns to leave their side four points behind.
Earlier on Saturday in the foursomes, Scott and Matsuyama lost two of the first five holes against Cameron Young and Collin Morikawa to par but won five successive holes from the ninth to move into a three-hole lead that they would not relinquish.
In the bottom match, Americans Finau and Max Homa were never behind against Si Woo Kim and Davis as they strolled to a 4&3 victory.
But KH Lee and Tom Kim came through a tough match with world number one Scottie Scheffler and Burns. There was never more than a hole between the players until Tom Kim holed a five-foot par putt to claim the 16th and move two ahead with two to play, and they wrapped up a 2&1 win on the 17th.
Both teams have lost players to the controversial LIV Golf circuit, with the International side arguably feeling the pain more. Open champion and world number three Cameron Smith, Chile’s Joaquin Niemann, Mexico’s Abraham Ancer, South Africa’s Louis Oosthuizen and Australia’s Marc Leishman are all missing.
The quintet are banned from playing, having opted to join Greg Norman’s Saudi Arabian-funded start-up, which has held five of its scheduled eight invitational events so far in 2022.
Captain Trevor Immelman has been forced to name eight debutants in his 12-strong International team.
The Americans are without Dustin Johnson, who won all five of his matches in last year’s record-breaking Ryder Cup victory over Europe at Whistling Straits.
Bryson DeChambeau and Brooks Koepka are other major winners who have left the PGA Tour to join LIV, but the US Presidents Cup side still contains 10 of the world’s top 16 players.