Tiafoe was outplayed in the first set but roared back to win 1-6, 7-6 (11), 10-8 to give Team World an unassailable 13-8 lead.
Team World, which had lost the four previous editions of the team event, began the day trailing 8-4, but Canada's Felix Auger-Aliassime stunned Novak Djokovic 6-3, 7-6 (3), having earlier partnered with Jack Sock in a 2-6, 6-3, 10-8 victory over Andy Murray and Matteo Berrettini.
Tsitsipas had the chance to take the match to a deciding singles clash, but Tiafoe looked inspired in front of a raucous crowd at London's O2 Arena who loved the American's showman antics.
After converting match point, he collapsed to the court and was buried under a pile of his teammates and captain John McEnroe, who then treated the crowd to some dance moves.
"It's an unbelievable feeling," Tiafoe, who reached the US Open semifinals earlier this month, said on court. "John McEnroe dropped a lot of F-bombs saying we can't lose again. Felix beat Novak today, and we all did it together. It wasn't just me."
McEnroe was overjoyed to have finally ended a long wait for victory and get one over old rival Bjorn Borg, who was captain of Team Europe, in the process.
"No one beats Team World five times in a row," McEnroe said. "Felix stepped up big time. Frances is prime time, we saw that at the US Open.
"This is an incredible team event, and I'm loving every second of it."