After losing his opener to Swiss Dominic Stricker on Tuesday, Draper's second match in the first-to-four-game format saw him defeat Hseng 1-4 4-2 4-3 (2) 4-2.
The 20-year-old said in quotes on nextgenatpfinals.com: "I thought Stricker played an amazing match yesterday, so all credit to him. I maybe wasn't at my best, but I thought he played an exceptionally good match so it was tough to go to sleep last night knowing that I played OK and still lost.
"Today I knew it would be a really tough match and I came out a bit slow but I had a good talking to myself and tried to really find a way. I was able to do that today so I'm really happy.
"It's a quick format, so you need to be sharp. When I sat down for the change of ends at the end of the first set, I had a real go at myself.
"I said 'you've got to be sharper, you've got to be more switched on and you've got to be alert out here', because it can go very quickly if you're not quite all there. So I'm glad I mentally turned things round."
Draper, the first British player to qualify for the event in Milan which began in 2017, will now face Italian Lorenzo Musetti on Thursday in his final group match as he bids to make the semi-finals.
At 41st and 23rd respectively, Draper and Musetti are the two highest ranked players at the tournament.