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Bautista Agut, who is the fifth seed in a draw featuring Dominic Thiem, Roger Federer and Andrey Rublev, was the highest ranked player in action in the round of 32 and fell behind to world number 39 Opelka.
Yet, the Spaniard pulled out his familiar battling qualities to prevailed over the big-serving American, who held sway 22-6 in the aces count.
Nevertheless, Bautista Agut was still able to fashion 11 break points over the course of the contest, converting one apiece decisively in sets two and three.
Alexander Bublik took the notion of big serves not being a decisive factor to an extreme as he popped in an underarm to fine effect on match point – qualifier Ramkumar Ramanathan scampering to thump his return out and conclude a 6-4 6-2 loss against Bautista Agut's next opponent.
The match between world number 42 Nikoloz Basilashvili and 41John Millman was as close as the rankings suggested, with the Georgian coming back to win 2-6 6-4 6-2.
Richard Gasquet and Taylor Fritz were straight-sets winners, with Rublev up next for Gasquet.
At this week's other ATP 250 event, the Open 13 Provence in Marseille, eighth seed Yoshihito Nishioka bowed out when he retired 2-6 2-4 down to Emil Ruusuvuori.
Wildcard Hugo Gaston beat Dennis Novak 3-6 6-4 6-1 to claim a notable scalp.
Top seed Daniil Medvedev, Stefanos Tsitsipas, Karen Khachanov and Ugo Humbert will enter the fray in the last 16.