All the goals on Saturday came in the second half, with Casemiro scoring a neat chip and a header bisected by Luuk de Jong's left foot finish for the visitors.
Sevilla were unhappy that the Dutch striker had a header ruled out in the first half after the VAR decided there had been an off the ball obstruction before he nodded home, although the VAR didn't rule out his goal after the ball appeared to hit the arm of his team-mate Munir, who was on the ground after a challenge, Xinhua news reports.
Real Madrid are now eight points clear of third-placed Atletico Madrid after the side, which they beat in last weekend's Spanish Supercup final, were beaten 2-0 in Eibar.
Atletico had won all of their previous eight visits to Eibar's Ipurua Stadium, but were undone by two goals which came from corners, with Esteban Burgos scoring from close range in the tenth minute and Edu Exposito netting Eibar's second in injury time as Atletico again looked short of firepower.
Aleix Vidal's goal on the break gave Alaves three important points as they won 1-0 away to Levante in a game where better finishing would have see Alaves win by a clearer margin.
There were no goals in a rainy El Sadar between Osasuna and Valladolid in a game where the home side finished stronger, after Sergi Guardiola had hit the bar for the visitors.
The round of games kicked off on Friday night as first half goals from Leonardo Cabrera, Nyom and Juan Mata gave them a 3-0 win away to near neighbors Leganes, who remain deep in the relegation zone.
FC Barcelona play their first game with Quique Setien in the dugout at home to Granada on Sunday night.
( With inputs from IANS )