Gaizka Toquero headed Athletic into a ninth-minute lead, but Yaya Toure equalised with a great solo goal and then Barca blitzed their rivals with three goals from Lionel Messi, Bojan Krkic and Xavi in 12 minutes to lift the cup for the first time since 1998.
It was coach Pep Guardiola's first trophy as a manager and Barcelona's first piece of silverware in two seasons although the Ligatitle could soon follow with only a point needed at Real Mallorca on Sunday to secure a 19th championship.
"We hope it's an historic week and we will go for the second title this weekend," said defender Gerard Pique. "We just want to enjoy this win first and then concentrate on trying to win more titles."
The final part of the treble - which no Spanish team has ever achieved - is the Champions League final against Manchester United on May 27.
For Athletic, who have won the cup 23 times, it was bitter disappointment in their first final since 1985.
Barcelona were without Andres Iniesta and Thierry Henry through injury so Bojan, 18, started the final.
At the back, Carles Puyol switched to left-back to replace the suspended Eric Abidal while midfielder Toure was deployed at centre-half.
The last time these two sides met in the final was back in 1984 when Athletic won 1-0 at the Santiago Bernabeu, although the game was remembered more for the post-match brawl between a number of players, including the great Diego Maradona in what was his final game for Barcelona.
There was little animosity between the two sides 25 years on although Barca were furious at the constant fouling suffered by Messi.
If Barcelona have a weakness it is set-pieces and Bilbao exploited that early on with Toquero heading in a whipped-in corner after just nine minutes.
It was just the start Barcelona didn't want although Guardiola's side should have equalised in the 19th minute when Samuel Eto'o, the league's top-scorer, got the ball caught up between his feet and the chance went begging.
Toure showed Eto'o the way forward after 31 minutes, surging from central defence before beating two Athletic players and then dispatching a fierce right-footed shot into the corner.
Messi twice went close to scoring early in the second half and finally got his goal in the 54th minute after Athletic failed to clear their lines.
Barca turned the screw with Bojan netting three minutes later with an immaculate finish after Athletic got caught out on the counter attack.
Xavi curled in a superb free-kick off the post in the 64th minute to torment Athletic further as Barca lifted their 25th Copa.