Tsitsipas - who suffered a shock defeat to Nishikori in Montreal in August - battled through two tight sets to win 7-6, 6-4.
"I'm glad of the win," Tsitsipas said on court afterwards, adding he had shown "great fighting spirit" towards the end.
"I'm pleased I managed to overcome the obstacle of Kei".
The Greek, once ranked third in the world, has slipped out of the ATP top 10 in recent months to now stand at 12th.
The loss in August to Nishikori, who is a former world number four but was ranked 576th at the beginning of the Montreal tournament, was followed swiftly by Tsitsipas dropping his father as coach after publicly criticising him.
"I did want to put out a fight and I wanted to show that I can go out there and play a good match against (Nishikori)," the 26-year-old said Friday.
The match was closely fought, with the first set ending with a nail-biting tiebreaker that could have gone either way.
"Being able to win (the tiebreaker), coming back and helping me win the first set was an important and critical moment," Tsitsipas told reporters after the match.
"Overcoming it was good, because it felt like I was able to restart now with a new mindset and it helped me get a bit of confidence."
In the second set, 34-year-old Nishikori, who has been plagued in recent seasons by injury, required a medical time-out.
Despite encouragement from the crowd, he never recovered his momentum and Tsitsipas won four of the last five games to close out the match.
