The Primera Liga triumph marked a second on the bounce for Marcelino Garcia Toral's men following a run of five games without a win, and was enough to move them above Malaga into fifth place in the standings.
Federico Fazioand Manu Del Moral had already put them in control before Kanoute's late flourish.
Getafehad the first chance through Nicolas Miku, whose shot was blocked in the box, but the hosts responded with Jesus Navas firing just wide and Alvaro Negredo also coming close.
Sevilla took the lead in the 32nd minute when Fazio headed home an Ivan Rakitic corner, although Getafe were unlucky not to level just before the break when Miguel Michel missed the target.
The hosts extended their lead four minutes into the second half when substitute Manu lashed home a shot from 20 yards into the top corner of the net to put them within sight of the three points.
Negredo and Kanoute both forced saves out of Getafe goalkeeper Miguel Moya while the visitors also continued to press and substitute Juan Rodriguez fired straight at home keeper Javi Varas.
Kanoute proved a constant danger in the dying minutes and finally got on the scoresheet in injury time when he reacted to sweep the ball home after a pass in the box from Rakitic.
The defeat brought Getafe back to earth after their stunning 1-0 home win over Barcelona at the end of last month, and left them perched in 16th position - just one point above the drop zone