Fils broke Nakashima's serve in the sixth game of the deciding third set, but the American broke back one game later to make it 4-3.
The third-set tie-breaker remained on serve until Fils broke through on Nakashima's serve to make it 6-5 and force match point. He finished the match on his own serve.
Fils saved 9 of 12 match points to reach the final where he will face No. 4 seed Francisco Cerundolo of Argentina, who was a 6-3, 6-0 winner over defending champion and second-seeded Cameron Norrie of Great Britain.
Gonet Geneva Open
Bulgaria's Grigor Dimitrov advanced to the final at Geneva, Switzerland, with a 3-6, 7-5, 7-6 (2) victory over No. 2 seed Taylor Fritz.
Dimitrov, the No. 4 seed, advanced to his first final in five years by saving 9 of 13 break points and overcoming 10 double faults.
Dimitrov will face Chile's Nicolas Jarry, who pulled off a 7-6 (3), 6-3 upset over Germany's Alexander Zverev, the No. 3 seed. Jarry broke Zverev's serve in the fourth game of the second set, the only break of serve in the match.
