Sevilla were under pressure after Valencia beat promoted Real Zaragoza 3-1 earlier on Sunday to climb above the Andalusians but Mali striker Kanoute rose unmarked to nod in Adriano Correia's cross for a 66th-minute winner.
Valencia striker David Villa netted his eighth of the season against Zaragoza to move clear in the scoring charts ahead of Barcelona's Lionel Messi and Zlatan Ibrahimovic on seven.
Champions Barca top the standings with 26 points from 10 matches, with Real Madrid on 25 and Sevilla on 22. Valencia are a point behind Sevilla in fourth while Villarreal are down in 16th place with just nine.
Brazil striker Luis Fabiano gave Sevilla the lead at the Sanchez Pizjuan with the first of his two goals after eight minutes before Robert Pires combined with Bruno Soriano to equalise for Villarreal just before the half hour.
The 36-year-old French midfielder ran on to Bruno's chipped return ball and volleyed superbly past Andres Palop.
Athletic Bilbao won 2-0 at Racing Santander and Sporting Gijon beat visiting Espanyol 1-0 thanks to a third-minute goal from Croatia striker Mate Bilic. Osasuna, who held Barca to a 1-1 draw last weekend, lost 2-0 at Hugo Sanchez's Almeria and Xerez climbed back off the bottom above Malaga with a 0-0 draw at Real Valladolid.
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