Gerardo Martino's men had bounced back from last weekend's shock defeat at Real Valladolid with a UEFA Champions League win over Manchester City on Wednesday.
And the reigning Spanish champions also put their league assault back on track with Lionel Messi the central figure in a comprehensive win.
The Argentinian's hat-trick saw him move ahead of Paulino Alcantara to become Barcelona's all-time leading goalscorer, with the latter's record of 369 having included goals in friendlies.
Alexis Sanchez, Andres Iniesta, Cristian Tello and Pedro were also on target as Barca moved back to within four points of leaders Real Madrid ahead of next weekend's Clasico at the Bernabeu.
Valencia's recent dip in form continued with a 1-0 defeat at Real Sociedad.
Juan Antonio Pizzi's men now sit 10 points behind Sociedad, who are fifth, after failing to win for a third league game in succession.
Imanol Agirretxe grabbed the only goal of the game in the 61st minute, ensuring Sociedad responded to back-to-back league defeats.
Having been beaten 2-0 by fierce rivals Real Betis in the first leg of their midweek UEFA Europa League tie, Sevilla moved up to sixth place with a resounding 4-1 home win over Real Valladolid.
Kevin Gameiro struck twice in between goals from Ivan Rakitic and Diogo Figueiras as Sevilla made it four league wins in a row.
Javi Guerra's late goal provided little consolation for the visitors, who failed to replicate their fine showing against Barca.
Elche and Betis played out a 0-0 draw at Estadio Manuel Martinez Valero.
Betis are now seven points adrift at the bottom of the table despite stretching their unbeaten run to five games in all competitions.
