Tsitsipas broke for 5-4 in the final set but struggled to finish the match. After a time violation and a double fault, Draper broke back with a forehand pass and then won the last three games to advance, ATP Tour reports.
Draper now leads Tsitsipas 2-0 in their ATP Head-2-Head series. The Stuttgart champion also beat the 11-time tour-level titlist at the Canadian ATP Masters 1000 event in 2022.
Draper will next play seventh seed Casper Ruud or Felix Auger-Aliassime.
In other three-set action, Ben Shelton saved a match point to overcome Tomas Martin Etcheverry 6-7(6), 7-6(7), 6-3 after two hours, 52 minutes.
The Argentine had a match point on serve at 7/6 in the second-set tie-break, after Shelton had three consecutive set points from 6/3.
Shelton will next face Hungarian Fabian Marozsan, who earlier upset eighth seed Grigor Dimitrov 4-6, 6-4, 6-3.
Holger Rune avoided such drama with a 6-3, 7-6(8) victory against Portuguese qualifier Nuno Borges. The 15th-seeded Dane fended off two set points in the second-set tie-break.
Rune next faces second seed Carlos Alcaraz or Gael Monfils.
