FCB held a lead heading into the clash as Luis Suarez's secured a 1-0 win at the Camp Nou in the first leg.
Five minutes into the second half, Philippe Coutinho scored his first goal for the club with a fine finish , 0-1.
Eight minutes were remaining when Suarez skipped past two defenders before picking out Rakitic, who calmly slotted past Domench, 0-2.
That proved to be Barca victory by 2-0 winners and an aggregate score of 3-0.
Copa Del Rey
Result: Valencia 0-2 FC Barcelona (Barca won 3-0 on aggregate)
Date: 08 February 2018
Venue: Mestalla