Real were thrashed 4-0 at Atletico Madrid on Saturday and Barcelona responded with a dazzling display at San Mames.
Lionel Messi opened the scoring with a deflected free-kick and the mercurial Argentinian, who was influential throughout, teed-up Luis Suarez to make it 2-0 after 26 minutes.
Mikel Rico pulled a goal back for Atletico in the 59th minute but, by the time home striker Artiz Aduriz netted seven minutes later, an Oscar de Marcos own goal and a sublime strike from Neymar had extended Barca's advantage.
Athletic finished with 10 men after Xabier Etxeita plunged his studs into Suarez's knee and the forward's replacement, Pedro Rodriguez completed the scoring when Messi crafted a wonderful 86th-minute effort.
Valencia replaced Sevilla in fourth after beating Espanyol 2-1, while Unai Emery's team went down at Getafe by the same scoreline.
The returning Pablo Piatti made the breakthrough for Valencia in the 62nd minute and the visitors went further ahead five minutes from time, when Dani Parejo's free-kick struck unfortunate goalkeeper Pau Lopez in the face and went in.
Sergio Garcia netted for Espanyol to set up a grandstand finish but Nuno's men closed out their fourth away win of the campaign.
Pedro Leon was Getafe's hero with an 85th-minute winner, condemning Sevilla to back-to-back defeats.
Grzegorz Krychowiak had initially pegged back Getafe after the hosts led through Alvaro Vazquez's 29th-minute penalty.
Elsewhere, Almeria claimed a vital 2-1 victory at fellow strugglers Cordoba.
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