Sevilla slip up against Deportivo
Striker Alvaro Negredo had the best chance to break the deadlock in the 65th minute at the Sanchez Pizjuan but Depor goalkeeper Manu, who made a string of fine saves, brilliantly blocked his close-range strike.
"We had loads of chances and played really well but the ball just wouldn't go in," Negredo said in a television interview, adding that the players had to forget their frustration and focus on Thursday's tricky Europa League clash at home to Paris Saint-Germain.
Atletico and Valencia, who both won on Saturday, have a perfect six points from two matches, with the Madrid club top on goal difference.
Villarreal claimed their first win of the season and warmed up for their Europa League match at Dynamo Zagreb with a thumping 4-0 win over Espanyol earlier on Sunday.
Italy striker Giuseppe Rossi set them on their way with a smart volley in the 23rd minute and added a third from the penalty spot in the 55th after Borja Valero's precise left-foot drive had beaten Carlos Kameni just after the half hour.
Brazil forward Nilmar added a fourth with just over 10 minutes remaining and Espanyol's miserable afternoon was completed when Francisco Chica was shown a straight red card for a wild challenge on Jefferson Montero.
In other matches, Malaga raced into a five-goal lead at Real Zaragoza after 34 minutes before conceding three second-half goals for a 5-3 victory.
Getafe thrashed promoted Levante 4-1 and Sporting Gijon saw off Michael Laudrup's Real Mallorca 2-0.
Champions Barcelona suffered a humiliating 2-0 defeat by promoted Hercules at the Nou Camp on Saturday, their first home league loss since May 2009.
Real Madrid ground out a laboured 1-0 victory over visiting Osasuna, a winning home debut for new coach Jose Mourinho, Valencia beat Racing Santander 1-0 and Atletico won a typically feisty encounter at Athletic Bilbao 2-1.