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 35 yards.
In the remaining two first legs on Thursday, La Liga strugglers Deportivo La 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 Copa 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.
The return legs, when most of the bigger clubs have home advantage, are in the week starting November 8.