Match scores: 1‑6, 6‑1, 7‑6 (3), 6‑2.
Shelton committed 14 unforced errors and two double faults in the first set.
He broke Griekspoor’s serve three times in the second set.
The third set was decided by a tiebreak, which Shelton won.
The match took place at Arthur Ashe Stadium in New York.
After a shaky start with many unforced errors and double faults, Shelton found his rhythm, improved his serve, and took control of the match.
The victory sets up a second‑round meeting with Poland’s Hubert Hurkacz.
Shelton aims to become the first American man to win the tournament since 2003.
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