The Basque side, who last won the trophy in 2015 with a 5-1 aggregate victory over the Catalans, grabbed a last minute equaliser through Asier Villalibre to tie the game at 2-2 and force an extra 30 minutes.
Antoine Griezmann had sent FC Barcelona ahead and restored their advantage with goals either side of Oscar de Marcos’s equaliser.
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Williams smashed into the top right corner from the edge of the penalty box three minutes into the additional period and Athletic Bilbao held on to win the trophy at Seville’s La Cartuja stadium.
There was late drama as FC Barcelona captain Messi received the first red card of his career as he swung an arm at Villalibre’s head in frustration in the dying moments of the clash.(dpa/NAN)