In the final set, 11th-ranked Tsitsipas broke for 5-4, but Draper closed off the match with 12 straight games to win 3-6 6-4 7-5.
“Today, I won the match thanks to my perseverance, tenacity, and mindset, and I’m really happy about that,” the world No. 28 player Draper stated in his on-court interview.
Next up for the 22-year-old is Felix Auger-Aliassime of Canada or Casper Ruud of Norway, who is ranked as the seventh seed.
Tsitsipas was competing in his first competition since ending his coaching relationship with his father Apostolos. He had previously finished second in the Australian Open and French Open.
Yulia Putintseva, the 34th-ranked player in the world, defeated defending champion Coco Gauff 6-4 6-2 6-4 in the first round of the women’s event.
Gauff, 20, stated, “I feel like I have to work on consistency, overall.”
The world number two ranking will be lost by the US Open champion to Aryna Sabalenka, who defeated Italy’s Elisabetta Cocciaretto 6-3, 6-4.
Elena Rybakina, ranked fourth, lost two match points before Leylah Fernandez of Canada advanced with a 3-6 7-6 (7-3) 6-4 triumph.
Karen Khachanov’s fourth-place finish in the world was beaten by Alexander Zverev 6-3 6-2, and Zhizhen Zhang of China was upset 6-4 6-3 by sixth seed Andrey Rublev.