Villarreal, who have played some of the best football in Spain this season, took the lead against another side expected to be pushing for a top four finish, after a superb run and pass from Brazil striker Nilmar in the ninth minute.
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Midfielder Cani profited to score with a neat touch and Italy striker Rossi twisted and turned in the area, beating three defenders, to net inside the near post after 52.
Villarreal climbed to second with 19 points from eight matches, one behind unbeaten leaders Real Madrid, who hammered Racing Santander 6-1 at the Bernabeu on Saturday.
Champions Barcelona are third on goal difference after their 2-0 victory at Real Zaragoza, also on Saturday.
Early pacesetters Valencia slipped to fourth with 16 points one ahead of Espanyol, who earlier kept pace with the top sides after a 2-1 victory at home to promoted Levante, thanks to goals from Jesus Datolo and Jose Callejon.
Atletico dropped to eighth with 13 points one behind Sevilla, who came out on top in the game of the day at the Sanchez Pizjuan where Luis Fabiano and Frederic Kanoute each scored twice in a thrilling 4-3 win over Athletic Bilbao.
Brazil striker Luis Fabiano, who has struggled for form this season, scored his first league goal of the campaign in the 35th minute and, after Mali's Kanoute had scored from the penalty spot, made it 3-0 early in the second half with a cool lob.
Bilbao's Spain striker Fernando Llorente continued his recent run of form by scoring twice in quick succession, in the 74th and 77th, with the hosts down to 10 men after a red card for Fernando Navarro.
A disputed penalty scored by Kanoute again, 10 minutes from time, appeared to have restored some order until a stoppage-time header from Bilbao's Igor Gabilondo set nerves jangling again among the home fans.
Elsewhere, Getafe beat Sporting Gijon 3-0 and Osasuna won by the same scoreline against Malaga, while the pressure remained on Almeria coach Juan Manuel Lillo after his side could only draw 1-1 at home to promoted Hercules.
