The Eagles lost their second straight Europa League final after Rodrigo and Oscar Cardozo both missed from the spot.
The Spanish club won the competition in successive years in 2006 and 2007 and celebrated lifting the trophy for a third time in eight years following a tense shootout at Juventus Stadium.
Goalkeeper Beto saved penalties from Oscar Cardozo and Rodrigo in the shootout, before Kevin Gameiro smashed in the winning kick to spark scenes of jubilation among Sevilla players and supporters.
Defeat for Benfica continued its European curse, with the Portuguese giant — which was beaten by an injury-time winner from Chelsea's Branislav Ivanovic in last season's Europa League final — now having lost all eight of its previous continental finals.
Former coach Bela Guttman famously decreed in 1962 that the club would wait 100 years for its next European title when he left the team in a dispute over pay — and that curse was extended in Italy.
The result also ends Benfica's hopes of a quadruple, although a domestic treble is still up for grabs, with Sunday's Taca de Portugal final still to come against Rio Ave.
The penalty kicks followed 120 minutes of evenly matched action, with both sides having chances to win the day before the dramatic denouement.
Benfica's Lima had a goalbound effort cleared off the line by Nicolas Pareja early in the second half, while Carlos Bacca wasted Sevilla's best chance in the first period of extra time, sending his effort just wide of goal after being played through by the outstanding Ivan Rakitic.
The first half-chance arrived in the 14th minute, with Benfica defender Ezequiel Garay unable to stab the ball home from a tight angle after Beto had parried Nicolas Gaitan's right-wing free kick into his path.
Alberto Moreno mustered Sevilla's first effort on target in the 37th minute but, after cutting in from the right side, his curling effort was comfortable for Jan Oblak.
Benfica twice tested Beto in first-half stoppage time, the goalkeeper first reacting well to parry Maxi Pereira's close-range effort before palming away Rodrigo's stinging drive as the second wave of attack arrived.
The Portuguese champion went close at the start of the second period, but was denied by last-ditch blocks on three occasions by some desperate Sevilla defending.
Maxi broke upfield and found Lima, who beat the keeper with his low shot, only for Pareja to clear just in front of the goalline. Pareja then blocked Rodrigo's rebound, before Jose Antonio Reyes denied Lima's effort as Sevilla somehow escaped unscathed.
Reyes was in action at the opposite end of the field shortly after, twice forcing saves from Oblak in quick succession.
Lima was then uncharacteristically wasteful once more, missing his kick after another lung-bursting run and pass from Maxi as both teams pushed for a late winner.
The Brazilian brought a spectacular save out of Beto with six minutes to go, cutting in from the left and unleashing a powerful drive that was tipped over by the keeper, before Garay headed over from an acute angle with Beto caught underneath the ball.
Garay then volleyed over from 12 yards in stoppage time after Sevilla failed to clear a corner, and that proved to be the last action of note in the 90 minutes as the game went into extra time.
Bacca missed a golden chance for Sevilla in the first period of the additional 30 minutes, firing narrowly wide of the left-hand post with the outside of his right foot after running onto a glorious first-time pass from Rakitic.
However, the Colombian was one of four Sevilla players to keep his cool from 12 yards to seal the Europa League title.