Atletico Madrid claimed the bragging rights with a 2-1 win at Real Madrid, while Neymar scored twice as Barcelona beat Athletic Bilbao.
Arda Turan came off the bench to earn the champions all three points from their derby clash in La Liga at Santiago Bernabeu, with the initial breakthrough arriving after just 10th minutes when Tiago headed home from a Koke corner.
Real fought their way back into the clash and had the chance to restore parity when Cristiano Ronaldo was clumsily tripped by Guilherme Siqueira in the penalty area.
Ronaldo – returning from injury – confidently beat Miguel Angel Moya from 12 yards in the 26th minute to level.
Karim Benzema wasted several opportunities to put Real ahead and Carlo Ancelotti's men were punished in the 14 minutes from time when substitute Arda scored the winner, rounding off a fantastic team move.
Luis Enrique's Barca side made it three wins out of three by beating Athletic 2-0 at Camp Nou.
The Catalan giants enjoyed significant spells of pressure and played some eye-catching football, but wasted numerous chances.
Athletic goalkeeper Gorka Iraizoz enjoyed an interesting duel with Munir El Haddadi, whom he denied on several occasions, and the former Espanyol man looked destined to claim a clean sheet.
Ernesto Valverde's Athletic rarely tested Claudio Bravo at the other end and they never looked capable of stealing a first league win at Camp Nou since November 2001.
Barca's woes in front of goal continued into the second period, but Neymar's entrance provided a much-needed impact as he opened the scoring with 12 minutes to go following a well-weighted pass from Lionel Messi.
Neymar made sure of the win a few moments later as he found the bottom-right corner, again after clever play by Messi, as Barca recorded an 11th successive league win over Athletic at Camp Nou.
Real Sociedad came from 2-0 down to salvage a 2-2 draw at Celta Vigo.
Jagoba Arrasate's men were 2-0 down to Real Madrid last time out before going on to win 4-2, and although they could not claim all three points in Vigo, they would have been relieved with a draw.
Goals from Fabian Orellana and Joaquin Larrivey gave Celta a deserved 2-0 lead early in the second half, but they failed to see out the match.
Imanol Agirretxe pulled one back with 21 minutes to go and then Jonny Castro turned Esteban Granero's cross past his own goalkeeper to gift the visitors a point in stoppage time.
The day's other fixture saw Malaga host Levante at La Rosaleda, with the match ending goalless.