The Mali striker's deft first touch and finish opened the scoring at the Sanchez Pizjuan and he rounded off a fine display with a sweeping volley and a powerful header.
Sevilla are third with 54 points, six ahead of fourth-placed Villarreal who beat Athletic Bilbao 2-0 at home with second-half goals from Santi Cazorla and Matias Fernandez.
Second-placed champions Real Madrid, with 60 points, play Almeria at the Bernabeu on Sunday when leaders Barcelona (66) welcome Malaga.
Valladolid's early ambition left them exposed when Ndri Romaric broke forward after eight minutes to feed Kanoute, whose first touch gave him space to finish low into the far corner.
Swedish striker Henok Goitom headed the visitors level from a freekick, but Kanoute put the home side back in front when he caught Jesus Navas's low cross with a perfectly-timed volley that flew inside the far post just before halftime.
Luis Fabiano broke the offside trap to round the keeper and make it 3-1 after the re-start.
The Brazil striker also headed against the post before Kanoute sealed his hat-trick with an unstoppable header from Fernando Navarro's cross in the 70th, taking his league tally for the season to 15.
An entertaining game at the Madrigal turned Villarreal's way when Giuseppe Rossi's diagonal run and pass found Cazorla unmarked on the edge of the area in the 69th minute, and the Spain winger drove a powerful shot wide of Gorka Iraizoz.
Athletic's response was hindered when Markel Susaeta was sent off soon after and the King's Cup finalists were condemned to their fourth successive defeat when Villarreal substitute Fernandez skipped round his marker to score at the end.
Athletic are now just five points above the relegation places in 13th.
