The former Tottenham striker netted the only goal of an eventful encounter as the Andalusians held on following two red cards and saw the visitors, down to 10 men, miss a penalty
Kanoute scored the winner last weekend at home to Real Sociedad and the Mali forward was on target again as Sevilla made it three wins and two draws from their opening five league matches The win saw Sevilla move provisionally up to second spot, behind city rivals Betis, while also ending Valencia's unbeaten start to the season.
Valencia came into this match off the back of an impressive 2-2 draw at home to Barcelona on Wednesday, but the Costa Blanca club had one eye on its midweek Champions League fixture against Chelsea and in-form striker Roberto Soldado was left out of the starting XI.
Sevilla was the better side early on and Kanoute converted after good work from Navas on 18 minutes.
Diego Perotti came close to doubling the locals' lead on two occasions as Sevilla dominated, but Valencia looked dangerous on the break as well and both Pablo Piatti and Jonas were denied by Javi Varas after the break.
Matters were complicated for the home side after Piotr Trochowski was sent off for a second yellow card, and even more so when he was followed by by Julien Escude, who brought down Aritz Aduriz and conceded a penalty.
However, Ever Banega's spot-kick hit the post and Aduriz was controversially dismissed moments later for a foul on Emir Spahic.
After that, Sevilla coped well and held on relatively comfortably for a morale-boosting victory.
The Andalusians move up to second for now, a point above Valencia - provisionally in third.