Valencia, Barca, Almeria and Celta de Vigo all progressed to the round of 16 with 24 goals scored across the four matches.
In Valencia, Rayo looked on track to triumph when they led 4-2 on the night and 5-4 on aggregate with just under 30 minutes remaining but goals from Paco Alcacer and Rodrigo saw the hosts win 6-5 over the two legs.
An own goal from Rayo defender Morcillo just after the break had dragged the tie to 4-4 - although the visitors led on away goals - and Adri Embarba's fine finish in the 61st minute put the Madrid-based club further on top.
Alcacer challenged Rayo goalkeeper Cristian Alvarez in the air, making contact with the gloveman, but the referee ignored the visitors' pleas for a foul, as Rodrigo smashed his volley into the net.
A much-changed Barcelona thrashed Segunda B leaders Huesca 8-1 to complete a 12-1 aggregate victory.
Pedro was the star for Luis Enrique's side - with Lionel Messi, Neymar and Luis Suarez all left out of the squad - with the 27-year-old scoring a hat-trick.
