Racing Santander and Levante shared the points in a 0-0 draw Sunday with both sides failing to chalk up their first win of the season while Betis saw off Mallorca with a late Ruben Castro goal to join Real Madrid and Valencia at the top of the league.
Santander were the better side in the first half with Adrian Gonzalez, Pedro Munitis and Manuel Arana all trying their luck from distance.
Levante goalkeeper Gustavo Munua had to save a Lautaro Acosta shot from close range on 31 minutes.
For Levante a Jose Barkero free kick tested Santander goalkeeper Antonio Rodriguez ?Tono' from 25 yards in the 32nd minute.
Acosta's pace caused problems throughout and he should have done better when he blazed over the bar from ten yards after breaking clear on 49 minutes.
Adrian came close again from long range on 66 minutes as Santander continued to press for a victory, but when their midfielder Papa Diop was given his marching orders on 81 minutes for a second yellow card all hope off a home win seemed to vanish.
Levante finished the stronger but both sides will have to improve if they are not to face a struggle for survival this season.
Betis meanwhile thanked a fine showing from Castro for their success. On 42 minutes he hit the post with a left footed shot from the edge of the area and Jorge Molina incredibly hit the bar twice in his attempts to convert the rebound.
Castro was always dangerous and went close again with a right-footed drive on 56 minutes.
Just as it seemed Mallorca would escape with a point, Castro finally appeared on 87 minutes to steer the ball home on the right side of the area from a corner.
On Saturday Real Madrid beat Getafe 4-2 to take an early two-point advantage over Barcelona at the top of the league after the Catalan side dropped points in drawing 2-2 away to Real Sociedad.
Elsewhere, Villarreal and Sevilla drew 2-2 and Valencia beat Atletico Madrid 1-0 to join Real Madrid at the top after two games.
For Madrid two goals for Karim Benzema, a Cristiano Ronaldo penalty and a late strike by substitute Gonzalo Higuain edged out a battling Getafe for whom Miku scored twice.
Barca seemed to have their game wrapped up with two early goals within a minute from Xavi Hernandez and Cesc Fabregas.
However, a sterling second half performance saw Sociedad level with headers on 57 and 59 minutes from Imanol Agirretxe and Antoine Griezmann.
Roberto Soldado's 52nd minute header won a tight game for Valencia to give them a 100% record.
Villarreal put up a battling performance, after losing goalkeeper Diego Lopez to a first half red card, to draw 2-2 with Sevilla.
After first half penalties for both sides were converted by Giuseppe Rossi and Alvaro Negredo, Villarreal substitute Marco Ruben put the home team ahead on 72 minutes before Alexis Ruano earned Sevilla a point with five minutes remaining.