In a game of few real chances, Kanoute capped a neat move with a powerful close-range finish eight minutes into the second half.
It was perhaps a fair result given that Sevilla had the better of the few openings on offer, but in truth there was little between the sides.
Sociedad had an early sight of goal when the ball was slipped in from the right to give Diego Irfan a good chance but his shot was charged down.
At the other end Piotr Trochowski then launched a long-range effort that went just wide.
Inigo Martinez had a chance for the visitors from a free-kick, but could not get enough on his header to turn it goalwards.
However, it was Sevilla who looked the more dangerous, and Alvaro Negredo was inches away from making proper contact after breaking free of the defence to meet Diego Perotti's clipped free-kick.
Gary Medel then forced a five save out of Claudio Bravo who got down low to turn his low shot around the post.
And moments later Bravo was busy again as Jesus Navas burst in from the wing to fire a low shot towards the corner of the goal.
The breakthrough came in the 53rd minute when Medel flicked the ball up and Negredo's header found the run of Kanoute who lashed it inside the near post.
The best chance of a leveller fell to Martinez, who got up to head Mikel Aranburu's dinked cross at the far post but could not find the target with the goalkeeper wrong-footed.
Instead, it was Sevilla who finished the strong with Navas and Negredo both having chances to add to the lead.