Seventh-seeded Coric felt at home with the weather, converting four out of 11 break points and scoring 35 winners to defeat his Spanish opponent.
"Conditions were very tough, but I like to play when it's like this, when the ball and court is slow, so I have more time," Coric said.
He next faces Britain's Aljaz Bedene. Sixth-seeded Phillip Kohlschreiber of Germany also advanced after saving five break points to beat Santiago Giraldo of Colombia 6-3 6-2.
Eighth-seeded Martin Klizan of Slovakia had to dig deep to defeat Pablo Carreno Busta of Spain 7-6 (3) 6-7 (8) 6-1. Both players exchanged breaks in the middle of the first set before the Slovakian prevailed in the tie-breaker.
Neither player was broken in the second set, with Carreno Busta winming the tie-breaker on his fourth set point. Klizan made the stronger start to the final set, winning the four opening games before sealing victory.
Andreas Haider-Maurer, Damir Dzumhur and Joao Sousa also advanced to the second round.
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