Santi Mina's header put Valencia ahead after eight minutes and Alvaro Negredo slotted home having been played in by Andre Gomes after 31 minutes.
Former England defender Neville, in his third match in charge of the Spanish team, decided against making too many changes despite a 3-1 lead from the first leg against the third-tier side.
Eibar overturned a 3-0 first-leg loss as a Mikel Arruabarrena penalty completed a 4-0 win over 10-man Ponferradina.
The top-flight side showed their priority was La Liga by resting nine players from the team that drew with Valencia on Sunday and still won, although the first-half dismissal of Jesus Berrocal made a big difference.
Ponferradina started stronger but were reduced to 10 men after Berrocal was given two yellow cards in succession for elbowing Aleksandar Pantic and arguing with the referee.
Borja Baston headed Eibar in front from a corner just before halftime and further goals came from Sergi Enrich and Simone Verdi before Arruabarrena converted a penalty.
Second-tier Mirandes knocked out Malaga as Lago Junior's goal secured a 1-0 win on the night and 3-1 aggregate triumph.
Oscar De Marcos hit a first-half opener as Athletic Bilbao hammered Linense 6-0 and went through 8-0 on aggregate.
Further goals came after the break from Javier Eraso, Xabier Etxeita, Kike Sola, Raul Garcia and Mikel Rico.
Rayo Vallecano advanced on goal difference against Getafe after losing 3-1 having won the first leg 2-0 while Las Palmas knocked out Real Sociedad after a 1-1 draw put them through 3-2 on aggregate.
Barcelona reached the last 16 after beating Villanovense in a tie brought forward due to their participation in the Club World Cup and Real Madrid were thrown out of the competition having fielded an ineligible player in their first-leg game against Cadiz. – Reuters
Original source: Neville bags first win as Valencia coach