A nervy start to the match from both sides was quickly forgotten as Valladolid took control midway through the first half when Oscar climbed highest in the box to head home from Marc Valiente's corner.
The hosts doubled their lead a minute later when Oscar stormed forward to launch a counter-attack before picking out Mojica, who calmly slotted home from inside the box.
Barcelona's defensive struggles invited more pressure from Valladolid, and they were gifted another goal when Frank Bagnack inadvertently put the ball into his own net as he looked to clear a dangerous ball.
It was 4-0 before the break as Andre Leao flicked on a corner at the near post to allow Oscar to grab his second goal of the evening from close range.
Valladolid continued to dominate after the interval, and they extended their lead further just before the hour mark when Carlos Pena's inviting cross was poked in at the back post by Jeffren, who piled more misery on his former side.
The emphatic victory was complete with two late goals as Mojica finished off another fast counter-attack by firing home his side's sixth goal of the night.
Substitute Zakarya Bergdich had the final say by firing home from a tight angle as the hosts cruised to all three points.