Barca had picked up their fourth trophy of the year in Tbilisi on Tuesday with a 5-4 win over Sevilla in extra time in the UEFA Super Cup.
But those exertions clearly took their toll as an under-strength side was dominated from the off by the Basques who exacted revenge for defeat in the Copa del Rey final back in May.
San Jose fired in a volley from just inside the Barca half to break the deadlock before Aduriz struck three times in 15 second-half minutes to give Ernesto Valverde's side a huge advantage heading into Monday's second-leg.
"We cannot think that Barca in their stadium can't score four goals. They are the best and capable of doing anything."
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Barca's defensive deficiencies had been laid bare in blowing a 4-1 lead against Sevilla that forced them into an energy-sapping extra 30 minutes in the Georgian capital.
However, with Gerard Pique among four first-team regulars rested the Catalans were even more of a shambles at the back and this time couldn't be rescued by an off-colour Luis Suarez and Lionel Messi.
"It is going to be difficult, but we have won many matches by many goals and we will try until the last minute," said a defiant Javier Mascherano.
"It is a one-off situation. They had four or five chances and scored four. Obviously that is not normal, especially given how we finished last season, but don't count us out yet.
"Now we have to correct what we did wrong, but above all prepare for the return leg.