Tiafoe, who has dropped only one set on his path to the last eight, will face Andrey Rublev in the next round. The Russian No 9 seed knocked out British No 1 Cameron Norrie in straight sets on Monday in a relatively easy victory.
As for Nadal, it means that the Spaniard will not be able to add to his 22 Grand Slams until the Australian Open at the earliest in January after his first defeat at Flushing Meadows since his semi-final loss in 2018.
The 36-year-old had missed the previous two tournaments through injury having beaten Daniil Medvedev in a thrilling final back in 2019. But the Mallorcan clearly did not look at his optimum fitness level as he struggled with excessive sweat during the match, while he walked off court for eight minutes after losing the sweat and returned with straps on his wrists.