The Spaniards had never won a UEFA Champions League match in England.
But they have now moved into the quarter-finals of Europe’s elite club competition for the first time since 1958, having drawn the first leg 0-0.
Jose Mourinho’s side were stunned by the two late strikes from Yedder and although Romelu Lukaku pulled a goal back, United’s once promising European campaign came to a sorry end.
Yedder put the visitors in front with a low finish just 87 seconds after coming off the bench in the 72nd minute.
The Frenchman scored again with a header that hit the underside of the bar and went in four minutes later.
“In spite of the fact we didn’t create chances in the first half, we were good, very good, up until the final third, and we gave Manchester United very little chance near our goal,” said Sevilla’s Italian manager Vincenzo Montella.
“Ben made the difference though, he was decisive, two times.”
Mourinho added: “I don’t think the performance was bad. I did my best, the players did their best. We tried, we lost and that’s football.
“We had chances to score and again in the second half we had chances but the first goal would always change the direction of the game.”
Manchester United were a shadow of the team which beat Liverpool in the English Premier League on Saturday, with sloppy passing and a lack of shape, urgency and fluency.
Questions will be asked as to why Mourinho switched around the team and formation from that game.
Marcus Rashford was moved to the right, Alexis Sanchez to the left and Jesse Lingard and Marouane Fellaini brought into midfield for Scott McTominay and Juan Mata.
However while United laboured, Sevilla had not looked a real threat in what was a generally poor quality game until the introduction of Yedder with 18 minutes left.
After a swift passing move, the forward sprung the defence with a sharp turn and fired a low shot past David De Gea.
He went on to double Sevilla’s lead with a back-post header which crossed the line off the underside of the bar in spite of the goalkeeper’s efforts.
Lukaku volleyed home from close range after Juan Mata had flicked on a corner in the 84th minute but there was to be no comeback for United.
The visitors could have added more.
Yedder, who now has eight goals from seven games in the UEFA 0Champions League this season, should have claimed a hat-trick.
This was when he was sent through one-on-one against De Gea, but he appeared to freeze and shot tamely straight at the goalkeeper.
That was quickly forgotten though as Sevilla’s players and fans wildly celebrated a famous win.
“We were just excellent, very good,” said Italian manager Vincenzo Montella. “A lot of those players played the game of their lives”.
Sevilla, who are fifth in La Liga, have never before reached the last eight in the Champions League, although they made the European Cup quarter-finals in 1958.(Reuters/NAN)