Australian Davis Cup star Jordan Thompson has progressed to the third round of the US Open for the first time.

Thompson overcame a third-set blip to beat Egor Gerasimov of Belarus 6-1 6-4 3-6 6-3 on Thursday to match his career-best grand slam run from the French Open in 2017.

The 26-year-old Sydneysider next plays either Mikhail Kukushkin or 13th seed Christian Garin on Saturday with the chance to reach the second week in New York.