"Sevilla of dreams," wrote Spanish newspaper AS, while Marca said "Nobody can forget your name."
Club president Jose Castro was overjoyed after the win over a United side full of internationals including Chile's Alexis Sanchez and their record signing Paul Pogba of France.
"A historic night of pure magic," said Castro. "We played a team decorated with big-money signings and superstars and we were better."
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Last season Sevilla came undone in the Champions League last 16 against unheralded Leicester City and had previously been beaten in England by Manchester City and Arsenal.
A scoreless first leg against United at the Ramon Sanchez-Pizjuan was followed up by a goalless first half in Manchester and the game looked destined for extra time before Montella threw on French striker Wissam Ben Yedder in the 72nd minute.
The forward drilled the ball home brilliantly to break the deadlock in the 74th and added another with a header in the 78th to ensure Sevilla will be in Friday's quarter-final draw.
Ben Yedder's introduction was the key to Sevilla's triumph, the 27-year-old forward netting his seventh and eighth goals of the competition to stun Jose Mourinho's team.
The Frenchman has struggled to make the first-choice lineup, with Montella starting Luis Muriel again despite his poor showing in the first leg, but took his chance with both hands.
"I'm very happy because he was the difference today and because recently he has suffered because of my choices," said Montella. "Ben made the difference, he was decisive two times."
While the other seven teams in the hat will hope to get Sevilla, who on paper are the weakest team in the draw, the win over United showed they can beat sides of greater stature.
Montella's side are only fifth in La Liga but sporting director Oscar Arias insists they are having a good season.
"Today we are in the King's Cup final and in the quarter-finals of the Champions League. It's a season like few others, to be valued."
(Editing by Ken Ferris)
