The 28th-ranked American was defeated by the 22-year-old 5-7 6-4 7-6 (7-1) after trailing in the first set.
In the third set, Draper served for the victory at 5-4, but Tiafoe broke the Briton’s serve, preventing Draper from converting a match point.
The sixth-seeded Draper blasted an incredible 31 aces to secure a matchup with American Brandon Nakashima in the semi-finals.
Due to a shoulder injury, Draper missed the entire grass-court season in 2017, but he is now expected to start Wimbledon as the top-ranked player in the United Kingdom.
Draper will take the top spot among Brits on Monday as a result of Cameron Norrie’s defeat against Jack Pinnington Jones at the Nottingham Open.
Rain stops the Nottingham Open’s play.
In the meantime, Katie Boulter was up 4-2 against Pole Magdalena Frech in the opening set of their Nottingham Open quarterfinal match.
Before the rain stopped play, the top-seeded British player had broken the serve of the fifth seed and advanced to another break point.
Fran Jones defeated American Ashlyn Krueger in three sets to book her spot in the round of eight before Boulter took the court on Friday.
The score was tied at 6-4 4-6 6-5 (30-30) when play was stopped on Thursday. Despite this, Jones managed to secure the victory.
