The hosts remain rooted in the bottom three and were left to rue Roberto Torres's missed penalty.
Atletico Madrid got back to winning ways and moved back into La Liga's top four as goals from Diego Godin, Kevin Gameiro and Yannick Carrasco ensured a comfortable 3-0 win at Osasuna on Sunday.
The hosts remain rooted in the bottom three and were left to rue Roberto Torres's missed penalty with the scores still level at 0-0.
Godin nodded home Koke's corner nine minutes before half-time and almost straight from kick-off Angel Correa released Gameiro to double Atletico's lead.
Substitute Carrasco rounded off the scoring with his eighth goal of the season in stoppage time.
"It was a very important game for us for the way in which we ended up playing," said Atletico coach Diego Simeone.
Atletico leapfrog Villarreal, who earlier lost 2-0 at home to Alaves, into fourth and move back to within nine points of leaders Real Madrid.
Third-placed Barcelona can close to within four points of Real ahead of next weekend's Clasico with a first victory in nine years at Real Sociedad later on Sunday.
"Oblak was decisive with the penalty save and after Godin's goal we felt more comfortable," added Simeone.
"In the second half we were a lot more organised and had more of a collective effort which allowed us to kill off the game."
Atletico had suffered back-to-back La Liga defeats for the first time in four years at the hands of Real Sociedad and Real Madrid in recent weeks.
Simeone therefore went back to his tried and trusted formula in search of a first clean sheet in six league games as Tiago and Jose Maria Gimenez were handed just their second league starts of the season.
Gameiro should have got Atletico off to the perfect start when he side-footed wide from point-blank range from Antoine Griezmann's inch-perfect cross.
However, Gimenez's recall at the expense of Stefan Savic nearly backfired when the Uruguayan was penalised for hauling down Oriol Riera inside the area after just 13 minutes.
Jan Oblak came to his side's rescue, though, as he sprung to his left to turn Torres's effort to safety.
Correa fired straight at Nazuet Perez from another great Griezmann pass as Atletico began to take control.
Yet, the opener arrived from another speciality of the Simeone era at Atletico as Godin rose highest to power home Koke's corner.
Osasuna were still recovering from that blow when Correa's chipped through ball allowed Gameiro to run in behind the defence and drill his shot low into the far corner.
Atletico controlled the game after the break and should have had a penalty of their own when Oier clearly handled while clearing off the Osasuna goal line.
Carrasco had surprisingly been left on the bench by Simeone, but made his presence count after coming on as he pounced on an error by Unai Garcia before firing low past Nazuet.