Nakashima, seeded 27th for the ATP Tour's final Masters 1000 event before the US Open in New York, won 6-7 (3-7) 7-6 (7-4) 6-1 in two hours 52 minutes on Tuesday (Wednesday AEST).
"Down match points, I was just trying to tell myself to keep fighting for every point," Nakashima said in his on-court interview.
"If he's able to close it out there, then too good. I just kept fighting and managed to get it to a third set. I'm super happy with the level in the third."
It was the 25-year-old's first win in four meetings against Medvedev, who beat the American in the Brisbane final earlier this year and had won 6-1 in sets against him entering the match.
Nakashima arrived in Cincinnati in strong form after reaching the semi-finals in Washington and Montreal, and improved to 10-2 on the summer hard-court swing with his victory.
The world No.22 will next face Nuno Borges after the Portuguese No.1 claimed a 6-3 6-4 upset of Russian 13th seed Andrey Rublev.
Australia's Adam Walton was also a third-round casualty, going down 6-4 4-6 7-6 (7-3) to Jaime Faria.
Walton broke in the 10th game to take the first set, but twice lost his serve in the second for the world No.79 from Portugal to level the match.
The 27-year-old Queenslander, who enjoyed comfortable wins in round one and two, took it to a deciding tiebreaker but lost the last four points to fall just short.
Elsewhere, there were straight-sets wins for the second, sixth and 10th seeds - Felix Auger-Aliassime, Taylor Fritz and Lorenzo Musetti.
The final contest of the day was a thrilling all-American clash between the 16th and 17th seeds, Learner Lien and Frances Tiafoe.
Tiafoe, eight years older than Learner, ran out a 6-4 4-6 6-4 winner and next faces Canadian Auger-Aliassime in the round of 16.
With AAP.
