Mauricio Pellegrino's men already had the template for how to beat Los Rojillos, having got the better of them with a 1-0 La Liga win at the weekend, and they followed the same pattern.
They had to wait until after the half-time break to move ahead, with Daniel Parejo scoring in the 47th minute, before talisman Roberto Soldado climbed off the bench to add a second which gives Los Che a handy cushion ahead of the return leg.
Parejo's goal was his first of the season at the 14th time of asking - while Soldado is no stranger to the back of the net, with his injury-time strike his 13th of the campaign already, but his first in the Copa.
Athletic Bilbao take on Eibar in a fourth-round clash on Wednesday night, while there are four fixtures in the fifth round.
Barcelona are at Cordoba, Real Madrid head to Celta Vigo, Atletico Madrid are at home to Getafe and Real Mallorca host Sevilla.