An 85th-minute goal from Rodrigo De Paul led Valencia to a 2-1 win at Rayo in the first leg of the round-of-32 tie.
It leaves Nuno Espirito Santo's men well-placed to advance to the last 16 in the all-La Liga tie.
But, despite not needing a victory at the Mestalla on Tuesday, Nuno said that would be the aim for his side.
"Now we have another game against Rayo in the Copa del Rey," he said after his team beat Rayo 3-0 in the league.
"Our aim is to win that one as well, so we will have to defend well and try to score - with the objective of continuing in the Copa del Rey."
Athletic Bilbao face a far tougher task at home to third-tier Alcoyano.
Ernesto Valverde's men were held 1-1 away from home in the first leg, needing a late equaliser from Borja Viguera to secure anything out of the clash.
A much-improved performance will be needed if Bilbao are to advance and avoid a shock exit.
Atletico Madrid carry a 3-0 lead back home against L'Hospitalet, but Diego Simeone's men needed three second-half goals in the first leg.
Barcelona are in complete control of their tie against Huesca, and they are likely to build on their 4-0 advantage.
Cordoba are 1-0 down but host Espanyol, while Villarreal are 2-1 up and host Cadiz.
Elsewhere, Espanyol host Deportivo Alaves holding a 2-0 advantage after Christian Stuani's first-leg brace.
Real Valladolid visit Elche after a first-leg 0-0 draw, while Malaga are at home after their 1-1 draw against Deportivo La Coruna.
Celta Vigo have suffered five straight losses heading into their clash against second-tier Las Palmas, who lead the tie 2-1.
Real Oviedo and Real Sociedad finished goalless the first time around, while Albacete and Levante drew 1-1.
Getafe are in control against Eibar with a 3-0 lead and Almeria host Real Betis having won their first leg 4-3.