Paris - Taylor Fritz put Team World to within one win of capturing their first Laver Cup after the American saw off Europe's Dominic Thiem 7-5, 6-7 (3/7), 10-8 in a barnstorming match in Geneva that leaves his side 11-7 up with two matches to play.
World had come into the day 7-5 down but were boosted by Rafael Nadal's withdrawal with a hand injury.
Fritz, himself a replacement for injured Nick Kyrgios, followed up on John Isner and Jack Sock's 5-7, 6-4, 10-8 defeat of Roger Federer and Stefanos Tsitsipas with a surprise tie-break triumph over world number five Thiem.
"That was such a big match for Team World to win, we really needed that," said Fritz.
"Now we're four points in the lead, one match from the win. It was so crucial.
"This has to be one of the biggest wins of my career. It means so much more when you're playing for other people as well."
John Isner will aim to seal the tournament win when he takes on Federer, but should the World number 20 lose to the 20-time Grand Slam champion Milos Raonic will have another chance against Alexander Zverev.
This year is the first time the tournament has been played since being added to the ATP Tour.
Europe won the 2018 edition 13-8 in Chicago.
Results from the third Laver Cup in Geneva on Sunday:
Roger Federer (Europe) bt John Isner (World) 6-4, 7-6 (7/3)
Taylor Fritz (World) bt Dominic Thiem (Europe) 7-5, 6-7 (3/7), 10-8
John Isner and Jack Sock (World) bt Roger Federer and Stefanos Tsitsipas (Europe) 5-7, 6-4, 10-8
Alexander Zverev (Europe) v Milos Raonic (World)
Overall score: World 11 Europe 10
Note: On opening day, each win secures one point, on second day, two points, on third and final day, three points.