Querrey advances to Nice quarterfinals
The third-seeded Querrey broke his opponent three times, while Stakhovsky converted only one of seven opportunities.
Querrey will play French wild card Edouard Roger-Vasselin, who rallied to defeat Ricardas Berankis 2-6, 6-4, 6-2.
Albert Montanes advanced to the last eight by beating Victor Hanescu 7-5, 7-6 (2), and Pablo Andujar routed Yen-Hsun Lu 6-2, 6-0.
Robin Haase was leading fourth-seeded John Isner 6-4, 1-4 when play was suspended because of rain.