Querrey overcame losing the first set and five match points in the third-set tiebreaker.
The 29th-ranked Querrey will face unseeded Ricardas Berankis of Lithuania, who advanced with a 6-3, 6-3 victory over Roberto Bautista Agut.
Querrey is one of two American players remaining in the Winston-Salem Open, the final hard-court tournament before the U.S. Open next week.
Qualifier Steve Johnson, who upset second-seeded Andreas Seppi of Italy on Tuesday, will face Chinese Taipei's Yen-Hsun Lu later Wednesday.
No. 22 Tommy Robredo and No. 27 Benoit Paire also will play later.