Alcorcon, a satellite town on the outskirts of Madrid, hit the headlines last season while still in Segunda B (Spain's third tier) when they humiliated La Liga giants Real Madrid 4-0 at the competition's same stage.
Real failed to turn the tie around at the Bernabeu and slumped to an astonishing 4-1 aggregate loss.
There was to be no repeat for a team now in the second division as Gurpegi grabbed the only goal in the 54th minute when he fired a shot in off the underside of the crossbar from around 30 metres.
In the remaining two first legs on Thursday, La Liga strugglers Deportivo Coruna came from behind to draw 1-1 at Osasuna and promoted Real Sociedad squandered a two-goal lead to lose 3-2 to visiting Almeria.
Real Madrid, who have not won the Cup since 1993, were held to a 0-0 draw at third tier Real Murcia on Tuesday, and 2009 winners Barcelona won 2-0 at Ceuta (Segunda B) despite fielding an almost completely second-string side.
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