In the men's singles, the struggling Tiafoe led 5-3 in the first set, but won just one more game in losing 7-6 (7-4), 6-0 to Cameron Norrie.
Roger Federer secured a return to the Hopman Cup final for Switzerland by defeating Greece's Stefanos Tsitsipas in straight sets on Thursday - but the United States exited the tournament despite the individual dominance of Serena Williams.
Later, the U.S. mixed doubles team comprising Williams and Frances Tiafoe faced a 4 (2)-3, 3 (4)-4, 1-4 defeat at the hands of British pair Boulter and Cameron Norrie resulting in Britain winning the tie.
The Britons claimed the tie with victory in the Fast4 mixed doubles 3-4 (2-5), 4-3 (5-4), 4-1.
"It was definitely good to play three singles matches here, and the mixed (doubles)", Williams said on-court after her singles match.
Williams dropped a set to Switzerland's Belinda Bencic on Tuesday, but beat Maria Sakkari of Greece in straight sets on Monday. The British pairing finished their Group B campaign with two wins and a defeat but did not do enough to progress to the final.
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Unseeded Jeremy Chardy of France defeated eighth-seed Nick Kyrgios of Australia 6-7 (5), 6-2, 6-3 to make the quarters. Italy's Marco Cecchinato received a walkover after his opponent Guido Pella of Argentina was forced to pull out.
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He rode his luck before being forced into a surprising dismount when he nicked a peach of a delivery from Shaheen Afridi. De Kock hit fours off his first two deliveries and never looked back as he raced to his half century off 59 balls.
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"I thought Stefanos came out and played a great match, so did I, very little unforced errors, just really good quality tennis", said Federer in his post-match interview.
The 23-year-old, who is ranked 14th in the world, has withdrawn from next week's Sydney International, which was set to be his final warm-up event before the year's first grand slam in Melbourne.
"I need to focus on my preparations for the Australian Open and do everything I can to be fit for the first grand slam of the year". The 17-time major champion hasn't played a competitive match since September but is confident he will be ready come the Australian Open on January 14.
Despite the USA's failure to make it out of the round-robin stage, Williams won all three of her individual outings as she gears up for the Australian Open.
Osaka's compatriot Kei Nishikori reached the last four in the men's singles as he won six of the last seven games to clinch a 7-5, 7-5 victory over 2017 champion Grigor Dimitrov.
Earlier, Norrie upset Tiafoe 7-6 (4), 6-0. Federer also posted the picture on social media, with the caption, 'Oh what a night.' 'He's the greatest of all time, to be honest.' 23-times Grand Slam victor Williams said. Third-seeded Hsieh Su-Wei also beat Olympic champion Monica Puig 6-1, 7-6 (3).