
The 20th-ranked Tiafoe made the last-eight by defeating Alexei Popyrin, who shocked defending champion Novak Djokovic in the last round, 6-4, 7-6 (7-3), 2-6, 6-3.
Tiafoe will face Bulgarian veteran Grigor Dimitrov for a place in the semifinals.
The 26-year-old is the second American man in the quarterfinals this year after Taylor Fritz defeated Casper Ruud earlier in the day.
Tommy Paul can make it three, but he has to get past world No 1 Jannik Sinner on Monday.
Roddick was the last American man to win a Grand Slam title when he claimed the US Open in 2003.
Tiafoe needed three match points to complete victory on Sunday while Australian Popyrin was left to regret squandering three set points in the second set.