Mali striker Kanoute was well-placed in the 25th minute to smash Luis Fabiano's headed pass into goal, canceling out Diego Rivas' opener from two minutes earlier.
Joseba Llorente caught Sevilla goalkeeper Andres Palop out of position to give Sociedad a 2-1 lead going into halftime, but Brazil striker Luis Fabiano started the rally in the 63rd by stabbing Alvaro Negredo's trickling shot over the line.
Kanoute received from Negredo two minutes later and sidefooted past Claudio Bravo inside the near post from a tight angle for his eighth of the season.
Sevilla's second straight win allowed it to join Getafe and Athletic in seventh place.
Spain midfielder Martinez snatched a point for the Basques by leaping high three minutes into extra time to deftly guide Igor Gabilondo's free kick beyond goalkeeper Sergio Asenjo with the back of his head.
Martin Demichelis' Malaga debut after joining on-loan from Bayern Munich looked to have gotten off to a perfect start as the Argentina defender headed home an 81st-minute corner kick to give the hosts the lead.
Malaga, in whose lineup Demichelis was one of four January transfer signings, created better chances throughout but would only move four points clear of the drop zone with the draw.