Gary Neville oversaw his first victory as Valencia coach after Barakaldo were defeated 2-0 with goals from Alvaro Negredo and Santi Mina.
Valencia advanced from the Round of 32 with a 5-1 aggregate win over the lower league club with two first-half strikes at Estadio Mestalla securing their route into the next stage.
Mina headed home the opener in the ninth minute before Negredo found the left corner from the centre of the area.
It was Neville's third game in charge at the Mestalla after opening his reign with a loss and a draw.
Getafe became the latest La Liga team to exit the cup competition despite a 3-1 victory over Rayo Vallecano, levelling 3-3 over the two legs but being knocked out on away goals.
Getafe stormed into a 3-0 first-half lead that raised hopes of reaching the next round, only for Lass Bangoura to tuck home in the 53rd minute and claim the crucial away goal.
Ivory Coast striker Lago Junior was on target in the 74th minute as Mirandes prevailed 1-0 at Malaga, winning the tie 3-1 on aggregate.
Athletic Bilbao romped into the next round with a 6-0 victory over Real Balompedica Linense, progressing 8-0 on aggregate.
There were six individual goalscorers with Xabier Etxeitia, Javier Eraso, Oscar de Marcos, Mikel Rico, Raul Garcia and Kike Sola on target.
Eibar overcame a 3-0 first-leg deficit to creep past Ponferradina 4-3 on aggregate on a nervy night at the Estadio Municipal de Ipurua.
Real Madrid's clash with Cadiz had been cancelled after the giants were expelled from the tournament for playing Denis Cheryshev in the 3-1 first-leg win when he should have been serving a suspension. The tie was awarded to Cadiz.
