Match ends, FC Sevilla 0(4), Benfica 0(2).
Sevilla beat Benfica on penalties to win the Europa League in Turin, their third triumph in the competition in nine seasons.
Benfica, losers in their seven previous European finals, were seeking a first continental trophy since 1962.
And the Portuguese side might have ended that sequence had Lima's late effort not been hooked off the line.
It fell to Kevin Gameiro to score the winning spot-kick after Sevilla keeper Beto denied Oscar Cardozo and Rodrigo.
Carlos Bacca, Stephane Mbia, who is on loan from Queens Park Rangers, and Jorge Moreno were also on target for the Spanish club.
Brazilian Lima and Luisao did find the net for Benfica but Lisbon-born Beto denied the side from his home city with crucial saves to keep out Cardozo and Rodrigo.
But while Los Rojiblancos's 9,000 travelling fans celebrated another triumph in Europe's second-tier club competition, Benfica's long wait for success on the continent continues.
Despite recently sealing a 33rd domestic title, their attempt to rid themselves of the increasingly troublesome "Guttmann curse" goes on.
Benfica's Hungarian coach of the early 1960s Bela Guttmann led the club to back-to-back European Cups but left shortly after the second of those triumphs when he was refused a pay rise.
Before going he declared that Benfica would never win another European competition without him at the helm. Fifty-two years on, they have still to prove him wrong.
Jorge Jesus's side had beaten Tottenham and Juventus on their way to the final, and were chasing a unique domestic and European quadruple.
A largely uneventful opening half came to life shortly before the interval, Beto saving from Benfica's Spanish forward Rodrigo at his near post moments after denying Maxi Pereira.
Then the Lisbon club were denied a stoppage-time penalty, German referee Felix Brych waving away strong Portuguese appeals after a foul on Nicolas Gaitan.
There was more action in the first five minutes of the second half than the previous 45 as Benfica carried on from where they left off.
Nicolas Pareja hooked Lima's shot off the line before Rodrigo's goal-bound attempt was charged down.
Sevilla responded with a sweeping move of their own, Moreno picking out Jose Antonio Reyes, but the former Arsenal striker's first-time shot produced a fine save from Jan Oblak.
Six minutes from the end of normal time, Benfica's Lima thought he had won it with a curling shot which Beto somehow managed to claw away.
Chances were few and far between in extra time as the players tired and nerves increased, though Bacca went close when he raced through on goal, only to fire his effort wide.
But Sevilla's frustration did not last long, as they sent their fans into raptures with four well-taken penalties to extend Benfica's European misery.
Sevilla manager Unai Emery:
"At times the game was totally even, but by the end they were doing most of the pushing.
"You could tell our players were suffering from fatigue and physical discomfort but this team has learned how to suffer.
"We have learned how to stay strong and so we were ready for that."
Benfica coach Jorge Jesus:
"We were better but in football, the best team doesn't always win. We had the more chances over 120 minutes but we didn't take them."
- 23Andújar MorenoBooked at 98mins
- 16MorenoBooked at 12mins
- 2FazioBooked at 11mins
- 19ReyesSubstituted forMarinat 78'minutesSubstituted forGameiroat 104'minutes
- 20Machín PérezSubstituted forFigueirasat 110'minutes
- 1Varas Herrera
- 3Navarro Corbacho
- 14Pereira Páez
- 16SiqueiraBooked at 30minsSubstituted forCardozoat 99'minutes
- 30André Gomes
- 4Luís da Silva
- 8SulejmaniSubstituted forAlmeidaat 25'minutesBooked at 100mins
- 11Lima dos Santos
- 20GaitánSubstituted forCavaleiroat 119'minutes
- 1De Morães Gusmão
- 33Nivaldo Vieira
- Dr. Felix Brych
- Shots on Target
Penalty Shootout ends, FC Sevilla 0(4), Benfica 0(2).
Goal! FC Sevilla 0(4), Benfica 0(2). Kevin Gameiro (FC Sevilla) converts the penalty with a right footed shot to the top left corner.
Goal! FC Sevilla 0(3), Benfica 0(2). Luisão (Benfica) converts the penalty with a right footed shot to the bottom right corner.
Goal! FC Sevilla 0(3), Benfica 0(1). Coke (FC Sevilla) converts the penalty with a right footed shot to the bottom left corner.
Penalty saved! Rodrigo (Benfica) fails to capitalise on this great opportunity, left footed shot saved in the bottom right corner.
Goal! FC Sevilla 0(2), Benfica 0(1). Stéphane Mbia (FC Sevilla) converts the penalty with a right footed shot to the top left corner.
Penalty saved! Óscar Cardozo (Benfica) fails to capitalise on this great opportunity, left footed shot saved in the bottom left corner.
Goal! FC Sevilla 0(1), Benfica 0(1). Carlos Bacca (FC Sevilla) converts the penalty with a right footed shot to the high centre of the goal.
Goal! FC Sevilla 0, Benfica 0(1). Lima (Benfica) converts the penalty with a right footed shot to the bottom left corner.
Penalty Shootout begins FC Sevilla 0, Benfica 0.
Second Half Extra Time ends, FC Sevilla 0, Benfica 0.
Delay over. They are ready to continue.
Delay in match Carlos Bacca (FC Sevilla) because of an injury.
Delay in match Ezequiel Garay (Benfica) because of an injury.
Offside, FC Sevilla. Ivan Rakitic tries a through ball, but Kevin Gameiro is caught offside.
Attempt blocked. Diogo Figueiras (FC Sevilla) left footed shot from outside the box is blocked. Assisted by Carlos Bacca.
Substitution, Benfica. Ivan Cavaleiro replaces Nicolas Gaitán.
Delay over. They are ready to continue.
Delay in match Beto (FC Sevilla) because of an injury.