The 24-year-old American, who has been in the spotlight since beating Rafael Nadal on the way to a first Grand Slam semi-final at the US Open last month, beat Spaniard Bernabe Zapata Miralles 6-1, 7-6 (9/7) in the second round in Tokyo.
The American breezed through the first set before Miralles fought back to take the second to a tie-break that saw some of the best rallies of the 1hr 32min encounter.
"Good match today, tough second set," said Tiafoe, who has won his last 13 tie-breaks.
"Sometimes it tips well your way. I'm playing very aggressive, I'm serving well in the tie-breaks, always a couple of aces."
He will face Miomir Kecmanovic in the last eight, after the Serb beat Britain's Dan Evans 6-3, 3-6, 7-6 (7/4).
After stunning Nadal at Flushing Meadows, Tiafoe played a starring role at the Laver Cup in London where his Rest of the World Team beat Europe for the first time in the competition's history.
But the fourth-seeded player, currently world number 19, said he was comfortable with all the attention he is receiving
"I don't really care about what other people think I should be doing because I've had recent success.
"You know: 'Oh, is he going to be the next...?'," he said.
"I've been on tour for seven or eight years now, none of that really moves me. I wanna win for me, I'm not trying to achieve anybody else's goals."
Tiafoe said his solid run since the US Open had been "great", adding that "I'm confident, and I'm just enjoying life".
