Fernando Lorente and Oscar De Marcos scored to complete Bilbao's rout of United and reached the quarter-finals of the UEFA Europa League.
Heading home after last week's stunning 3-2 win at Old Trafford, Marcelo Bielsa's men dominated again with Llorente firing a stunning volley to extend his side's aggregate lead in the 23rd minute.
Andoni Iraola, Markel Susaeta and Gaizka Toquero all missed chances to put their side further ahead before De Marcos effectively sealed United's fate with a 65th minute effort to put them up 2-0 on the night and 5-2 on aggregate.
Wayne Rooney responded with a superb volley 10 minutes from time but it was too little, too late for Sir Alex Ferguson's men, whose season of continental misery ended in a 5-3 aggregate defeat.
Manchester City's storming second-half fightback at the Etihad Stadium proved all in vain as they were knocked out on the away goals rule by Sporting Lisbon after a 3-3 aggregate finish.
The visitors looked set to coast into the last eight as early strikes from Matias Fernandez and Ricky van Wolfswinkel sent them 2-0 up at the break, giving them a 3-0 overall lead.
But City blasted back to win 3-2, with two goals from Sergio Aguero sandwiching a Mario Balotelli penalty. Keeper Joe Hart came close to heading a dramatic injury-time clincher but Roberto Mancini's men bowed out.
Dutch Eredivisie leaders AZ survived the third minute sending-off of Nick Viergever as they clung on for a 2-1 defeat at Udinese which was enough to send them through 3-2 on aggregate.
Viergever's early dismissal threw AZ into chaos and things looked bleak when two goals from Antonio Di Natale drew the hosts level on aggregate within the opening 15 minutes.
But Udinese failed to make the most of their chances and AZ went back in front through a 31st minute strike from Erik Falkenburg, before managing to hold on for a last eight place.
Hannover left no room for doubt with a crushing 4-0 second leg win over Standard Liege in Germany to send them through to the quarter-finals 6-2 on aggregate.
Mohammed Abdellaoue opened the scoring on four minutes before two own goals from Brazilian Kanu either side of the break. Sergio Pinto added a fourth in stoppage time after Standard had Serge Gakpe sent off.
Former winners Valencia moved through 5-3 on aggregate after a 1-1 draw at PSV. Adil Rami opened the scoring for Valencia on 47 before Ola Toivonen equalised. Goalscorer Rami was sent off in injury time.
Ukrainians Metalist Kharkiv staged a fine late comeback to nudge out Olympiacos with a 2-1 win in Greece enough to see them through on the away goals rule after a 2-2 aggregate result.
Ivan Marcano's early goal put Olympiacos further ahead on aggregate but Cristian Villagra equalised on the night in the 81st minute and Marko Devic scored the all-important winner four minutes from time.
A Klaas Jan Huntelaar hat-trick helped Schalke also come back from behind to beat Steve McClaren's FC Twente, with a 4-1 win on the night giving them a 4-2 aggregate win.
Willem Janssen had extended Twente's advantage with a 14th-minute opening strike, but Huntelaar equalised on 29 and added two further second-half goals either side of a 71st-minute effort from Jermaine Jones.
Atletico Madrid wrapped up an impressive 6-1 aggregate win over Besiktas with a 3-0 win in Turkey. Adrian Lopez put the Spaniards ahead before late goals from Radamel Falcao and Eduardo Salvio completed their easy passage.
Thursday's Europa League Results
Athletic Bilbao 2-1 Manchester United (agg 5-3)
Manchester City 3-2 Sporting Lisbon (agg 3-3a)
PSV Eindhoven 1-1 Valencia (agg 3-5)
Besiktas 0-3 Atletico Madrid (agg 1-6)
Schalke 4-1 FC Twente (agg 4-2)
Udinese 2-1 AZ Alkmaar (agg 2-3)
Hannover 4-0 Standard Liege (agg 6-2)
Olympiacos 1-2 Metalist Kharkiv (agg 2-2a)