Sevilla can now concentrate on the Copa del Rey final and making up the two-point deficit on leaders Real Madrid in the four Liga fixtures remaining this season as they chase an inredible treble.
The trophy looked to be heading to Andalucia when Kanoute prodded home in the 105th minute to put Sevilla 2-1 up, but Domingos Jonatas' thundering low strike with just four mintues remaining ensured penalty drama.
Goalkeeper Andres Palop, whose headed goal against Shakhtar Donetsk in the last 16 had kept the holders in the competition, saved spot-kicks from Luis Garcia, Jonatas and Marc Torrejon as Sevilla emulated Real Madrid's successive UEFA Cup triumphs in 1985 and 1986.
Sevilla had taken the lead in the 18th minute thanks to a superb counter-attack goal from winger Adriano Correia.
Adriano curled a shot low into the far corner after being putting in the clear down the left flank when keeper Andres Palop collected a corner inside his own area and hurled a long throw into his path.
But Espanyol got back into the match with Albert Riera's strike just before the half hour, the winger cutting inside from the left and beat Palop with a right-foot effort that deflected off the foot of full-back Daniel Alves and flew high into the far corner.
Riera almost put Espanyol in the lead after the break when he tried his luck with a dipping volley from distance which Palop tipped on to the bar and over for a corner.
But Moises Hurtado's second booking of the evening in the 67th minute left the underdogs down to 10 men and with their backs against the wall, prompting Espanyol coach Ernesto Valverde to sacrifice captain Raul Tamudo in an effort to give his side more cover in midfield.
Sevilla began to get on top as 90 minutes approached. In the 77th minute substitute Alexander Kerzhakov blasted over from close range before Javi Navarro headed straight at the goalkeeper from 10 yards out.
Freddie Kanoute then had a close-range effort saved by goalkeeper Gorka Iraizoz, Kerzhakov firing the rebound high over the bar from a tight angle as Espanyol hung on and took the game in to extra-time.
Sevilla continued to press hard, and had several chances to edge in front before Kanoute finally broke Espanyol's resistance, prodding a low left-wing cross home from close range.
Iraizoz was forced in to further stops in the second half of extra-time as Sevilla threatened to add a third to kill off the game, most notably a save with his legs as Antonio Puerta fired a low shot goalwards from eight yards out.
And the goalkeeper's heroics proved decisive as Jonatas slammed a 25-yard drive low in to the corner with just four minutes remaining to send the match in to penalties.