Pep Guardiola has gone out on a high after guiding Barcelona to their 26th triumph in the Copa del Rey.
Pedro gave Barca the best possible start after two minutes when he struck home after the ball had broken to him inside the area.
Lionel Messi beat Gorka Iraizoz from close range to make it 2-0 in the 20th minute, before Pedro doubled his tally for the night four minutes later.
Bilbao were denied a penalty after the referee waved off Gerard Pique's challenge on Fernando Llorente after 27 minutes.
The second half was much tighter, with neither side creating any clear-cut chances.
Iraizoz denied Messi after the Argentine had slalomed through the Bilbao defence, saving well down low with his foot.
Iker Muniain tested Manuel Pinto as Marcelo Bielsa's side searched for a consolation goal, but Barcelona's defence held out to give Guardiola the perfect send off.
