Barcelona overcame derby rivals Espanyol 1-0 at Camp Nou, while Real Madrid beat Valencia 3-2 at La Mestalla.
Barcelona equalled a club record of 15 consecutive matches unbeaten with a 1-0 win over Espanyol at Camp Nou.
Zlatan Ibrahimovic's controversial first-half penalty proved to be enough to give Pep Guardiola's troops the three points.
The Swede smashed home from the spot after Jose Baena had been adjudged to have fouled Xavi inside the box.
Barca dominated for most of the game, but they could not add to their lead in the absence of injured star Lionel Messi.
Ezequiel Garay's late goal earned Real Madrid a 3-2 win over Valencia at La Mestalla.
After a goalless first half Gonzalo Higuain broke the deadlock on 54 minutes when he headed home Karim Benzema's cross.
Valencia hit back six minutes later when David Villa headed home Jeremy Mathieu's cross only for Higuain to restore Real's lad five minutes later with a clincial finish from Marcelo's pass.
Joaquin drew Valencia level for a second time on 80 minutes with a drilled finish past Iker Casillas.
However, Real grabbed the winner three minutes later when Garay headed home Xabi Alonso's free-kick to keep them on the tails of Barcelona.
Athletic Bilbao piled the misery on struggling Real Zaragoza with a 2-1 win at La Romareda.
Mikel San Jose broke the deadlock on the hour mark when he headed home Iker Muniain's cross.
Markel Susaeta added a second nine minutes from time when he converted Muniain's through ball.
Zaragoza set up a dramatic finale when Carlos Diogo reduced the arrears in the dying seconds, but Bilbao held on for the victory to increase the pressure on under-fire Zaragoza coach Marcelino.
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