Querrey won the first set 6-2 and was tied 2-2 in the second when his opponent, fellow American Michael Russell, retired with an injury after just 44 minutes.
Croatia's Ivan Dodig cruised past Ukraine's Dolgopolov 6-3, 6-3, winning 12 of the last 15 games en route to the 57-minute triumph.
Also notching Day 1 victories were No. 8 seed Xavier Malisse of Belgium, who breezed past Alejandro Falla of Colombia 6-3, 6-3, and Russian Evgeny Donskoy, who bested Belgium's Steve Darcis 7-6 (7-5), 6-3.
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