Shelton, a 21-year-old left-hander from Atlanta, won his only ATP title at last October's Japan Open, but hopes to duplicate the feat on clay in the Houston, Texas, event.
It took five match points for Shelton, who won all seven break points he faced, to finally subdue Nakashima after two hours and 13 minutes.
"Definitely not an easy matchup today with the way Brandon was serving and playing," Shelton said. "He made things really difficulty and I was definitely feeling the pressure in that tie-break. But I'm really happy to get through."
Next up for Shelton will be Argentine fourth seed Tomás Etcheverry, who advanced 6-3, 0-1 when US opponent Michael Mmoh retired from the match.
Etcheverry was a finalist at last year's US Clay Courts, falling to American Frances Tiafoe in two tie-breakers in the championship match.
Italy's unseeded Luciano Darderi booked a semi-final berth by upsetting US seventh seed Marcos Giron 6-0, 6-4.
Darderi will next face third-seeded Tiafoe in the other semi-final.
