Draper, who withdrew during his quarter-final against Hugo Humbert at the ATP Tour event in Tokyo last month with an abdominal injury and then withdrew from the Shanghai Masters, won 7-6 (5) 7-5.
The British No 1 was forced to dig deep in a contest that lasted one hour and 37 minutes, fighting back from 5-3 down in the first set to force a tiebreak where he trailed 3-1 before prevailing.
A second set ensued and Nishikori made an error while serving to stay in the contest, saving one match point, but then sent a long forehand from the next to give Draper the win.
Draper will next face Italian Luciano Darderi, who beat former world number three and 2020 US Open champion Thiem 7-6 (6) 6-2 to complete the Austrian’s professional journey.
Thiem, whose career has been marred by injuries since his only Grand Slam triumph, announced in May that this season would be his last and he led 4-2 in the first set, then 3-0 and 5-2 in the break.
But world number 42 Darderi fought back to take the first set, then comfortably won the second, with the crowd holding up special cards with the Austrian flag and the words “Danke Dominik” (Thank you, Dominik) after the match.
Thiem, a 17-time winner on the ATP Tour, then placed the racket he played with in a special glass case to be auctioned off.
The 31-year-old, runner-up at the French Open twice and the Australian Open once, said: “I’ve had so many nice goodbyes over the last few months, but today I want to thank you for all the sensational years.
“I’m just part of this career. The whole trip was an absolute dream and I want this afternoon, this evening to be yours. I couldn’t have imagined it better. Thank you.”
Elsewhere on Tuesday, Britain’s Cameron Norrie lost 6-4 7-6 (4) to American Francis Tiafoe.