Alexander Zverev won a deciding rubber against Milos Raonic in Switzerland to earn Team Europe a dramatic 13-11 win over Team World in the Laver Cup.
Zverev beat Raonic 6-4 3-6 10-4 for Team Europe's third victory in a row.
Team World were 7-5 down overnight but John Isner and Jack Sock overcame Roger Federer and Stefanos Tsitsipas 5-7 6-4 10-8 in the doubles to put them 8-7 up.
Isner and Sock improved to 3-0 in Laver Cup doubles, and the 30th-ranked Fritz overcame Austria's Thiem.
"This has to be one of the biggest wins of my career," Fritz said. "I'm the kind of person that really doesn't want to let my team down."
Fritz secured a narrow 7-5 6-7 (3-7) 10-5 victory over Thiem, while 20-time Grand Slam winner Federer, playing in his home country, claimed a 6-4 7-6 (7-3) win over Isner in Geneva.
Both sides had player withdrawals for injuries on the final day, with Rafael Nadal pulling out for Team Europe and Nick Kyrgios for Team World.
Strong play from the Americans on Sunday gave the world team an overall lead for the first time in the three-day competition.
Nadal was supposed to partner Federer in the doubles and face Kyrgios in a singles tie.
The Spaniard was replaced by Tsitsipas in the doubles, while Thiem came in for him in the singles ties - in which Fritz stood in for Kyrgios.
With Europe needing to sweep the last two rubbers, Federer came through in a typically tight match against Isner with few break-point chances.
"I'm thrilled that I was able to give something back to the team," Federer said.
"Obviously to see Rafa on the sidelines after having to pull out with an injury, it's great camaraderie I feel."
Team World have yet to win the competition since its inception three years ago.
"I'm very proud of my team," said Team Europe skipper Bjorn Borg. "I'm a very happy captain."