World number 67 Bedene beat the Spaniard 7-6 (7-2) 7-6 (9-7).
The Slovenian-born Briton, who reached the second round of Wimbledon, beat Spain's Daniel Gimeno-Traver - also in straight sets - in the first round.
Bedene, 26, set up a meeting with Fabio Fognini in the Hamburg Open Quarter-finals.
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