The American's departure means only two of the eight seeds are still standing in Tokyo.

Top seed Taylor Fritz, number three Casper Ruud, fourth seed Stefanos Tsitsipas and number seven Frances Tiafoe all lost in the first round.

Hubert Hurkacz, seeded two, was beaten by Britain's Jack Draper in the second round.

Paul joined them after letting the Czech Republic's Machac back into a match that the American looked to have total control of.

"Even the not-seeded players here are great," said the 23-year-old Machac, who has a world ranking of 34 and is looking to win his first career title.

"I'm just happy that I'm in and I just try to believe as much as possible."

Paul won five straight games in the first set but Machac came roaring back in the second and dug in when he found himself 3-0 down in the final set.

He will play Australia's Christopher O'Connell or American Alex Michelsen in the quarter-finals.

"I feel great," said Machac.

"First set he was better, second set I found my rhythm. In the third set I was playing unbelievable so I'm super-happy with my performance."

(For more sports news and updates, follow Ahram Online Sports on Twitter at @AO_Sports and on Facebook at AhramOnlineSports.)