Lionel Messi had given the European champions -- who trailed 4-0 from the first leg -- a glimmer of hope with the opener two minutes before half-time on Monday.
However, any realistic hope Barca had of pulling off a monumental comeback disappeared when Gerard Pique was shown a straight red card for dissent 10 minutes into the second-half.
And Aritz Aduriz exploited the space left by the Spanish international defender's dismissal to follow up his hat-trick in the first leg with the crucial away goal midway through the second-half.
The hosts started on the front foot as Luis Suarez saw a shot deflected just over before Pique's effort came back off the crossbar.
Yet, Athletic's mass ranks of defence were comfortably keeping Enrique's men at bay and the visitors even had a great chance to put the tie to bed when Javier Eraso skipped past Javier Mascherano before firing into the side-netting rather than squaring for Aduriz to apply a simple finish.
Claudio Bravo kept Barcelona's hopes alive early in the second period with saves from Markel Susaeta and Aduriz, but the Chilean's good work was undone when Pique was sent-off for something he said to the referee's assistant after he failed to flag Aduriz offside.
To their credit Barca didn't give up as Pedro Rodriguez, Ivan Rakitic and Suarez all fired off target with fine chances to reduce the deficit to two goals.
However, Athletic struck the final blow when Aduriz was given acres of space to latch onto Eraso's flick-on and he slotted into an empty net at the second attempt after Bravo had saved his first effort.
Defeat ends Barcelona's hopes of matching the club record set by Pep Guardiola's side in 2009 of winning six trophies in a calendar year.
They won't have long to wait for a chance at revenge, though, as the two sides square off once more in their opening game of the La Liga season on Sunday in Bilbao.
You’ve reached your limit of {{free_limit}} free articles this month.
Subscribe now for unlimited access.
Already subscribed? Log in
Subscribe to read the full story →
Smart Quarterly
₹900
3 Months
₹300/Month
Smart Essential
₹2,700
1 Year
₹225/Month
Super Saver
₹3,900
2 Years
₹162/Month
Renews automatically, cancel anytime
Here’s what’s included in our digital subscription plans
Exclusive premium stories online
Over 30 premium stories daily, handpicked by our editors


Complimentary Access to The New York Times
News, Games, Cooking, Audio, Wirecutter & The Athletic
Business Standard Epaper
Digital replica of our daily newspaper — with options to read, save, and share


Curated Newsletters
Insights on markets, finance, politics, tech, and more delivered to your inbox
Market Analysis & Investment Insights
In-depth market analysis & insights with access to The Smart Investor


Archives
Repository of articles and publications dating back to 1997
Ad-free Reading
Uninterrupted reading experience with no advertisements


Seamless Access Across All Devices
Access Business Standard across devices — mobile, tablet, or PC, via web or app
