The 28-year-old Australian world No.87 has lost ten of his 17 matches this year.
He pushed Ramos-Vinolas, No.31 in the world, hard, but lost 4-6 6-3 4-6 in 129 minutes.
Thompson made a flying start, winning eight of the opening ten points to take a 2-0 lead. But Ramos-Vinolas immediately broke back and did so again in the seventh game, taking it on the third break point after racing to 40-0.
The Spaniard gave Thompson no chance of levelling, dropping one point in his next two service games to secure the set in 39 minutes.
The second stanza went with serve until Thompson broke unexpectedly in the eighth, a double-fault at 40-0 by his 34-year-old opponent opening the door. Thompson won the next five points to break, then served out to 15.
With momentum behind him Thompson broke early in the third and took a 3-1 lead but, then his form went awry. Ramos-Vinolas won five of the next six games, clinching the tie on his third match point.
On a day of minor surprises the veteran Frenchman Richard Gasquet beat America's Tommy Paul 7-5 6-2, top-40 player Lloyd Harris went out to lucky loser Carlos Taberner 6-3 6-4, and Bolivian qualifier Hugo Dellien beat experienced Jiri Vesely 6-3 6-3.
Former world No.3 Dominic Thiem, still working his way back to form and fitness after injury, lost to Benjamin Bonzi 6-3 7-6 (9) after a lengthy second-set tie-break in which he had three set-point chances to extend the match.
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