Youth team coach Nico Estevez took charge for the fourth-round tie following Miroslav Djukic's departure on Monday and, after the first leg was goalless, saw Paco Alcacer net the decisive goal in the 37th minute to see them into the last 16.
Iker Muniain scored twice as Athletic Bilbao comfortably turned around a 1-0 first-leg defeicit against Celta Vigo.
The Basque club, fourth in the Primera Division, won 4-0 on the night with Markel Susaeta and Aritz Aduriz also on target.
Celta's task was made more difficult when Hugo Mallo saw red on 53 minutes, although Athletic did not make the tie safe until Muniain and Aduriz scored in the final 10 minutes.
Rayo Vallecano also needed late goals from Adrian and Alberto Bueno before they progressed 3-1 against Valladolid.
Valladolid led 1-0 on the night, and in the tie, when Javi Guerra scored after 28 minutes.
Adrian levelled four minutes later before snatching the lead three minutes from the end. Substitute Bueno ensured Rayo's progress in injury time.
Espanyol won 2-0 at home to Jaen to progress 4-2 on aggregate.
Simao Sabrosa fired them ahead in the tie on 12 minutes before Sidnei wrapped up matters five minutes from the end.