(CNN) -- Athletic Bilbao sent Manchester United crashing out of the Europa League on Thursday with a 2-1 win in the second leg of their last-16 tie at the San Mames Stadium.
Fernando Llorente put the home side in front in the 24th minute with a stunning right-foot volley before Oscar de Marcos doubled the lead 20 minutes into the second half.
In between Athletic dominated possession, squandering a host of chances to put the tie well beyond the reach of United.
Wayne Rooney's 80th-minute strike offered United's traveling fans a glimmer of hope that a famous fightback might be mounted but it never materialized as the home side cantered to a 5-3 aggregate win.
"The team played a memorable game," said goalscorer Llorente.
"I don't know if it's my greatest moment with the club. But it's the first time that we've gone past the last 16 in the Europa League, and that's incredible," the Spanish striker added.
Manchester City looked to be heading for an equally humbling defeat before almost staging an incredible comeback against Portugal's Sporting Lisbon at the Etihad Stadium.
Trailing 1-0 from the first leg, Roberto Mancini's side conceded two first-half goals.
A sublime free kick from Chile international Matias Fernandez in the 24th minute stunned home fans and then Ricky van Wolfswinkel converted Marat Izmailov's cross to make it 2-0 five minutes before the break.
At 3-0 down on aggregate City looked dead and buried but somehow managed to claw their way back into the tie.
Sergio Aguero fired home on the hour mark before Mario Balotelli provided a cool finish from the penalty spot 15 minutes later.
Aguero was on hand again in the 82nd minute, slamming home from close range to make it 3-2 to City on the night and set up a breathless climax.
City surged forward in search of a fourth goal as Sporting frantically tried to clear their lines.
In the dying seconds, Joe Hart charged upfield for the final corner of the match and nearly headed City into the quarterfinals, but his opposite number Rui Patricio managed to deflect the ball inches wide of the post, sending the Portuguese side through on away goals.
La Liga's third place side Valencia also progress to the last eight thanks to a 1-1 draw against the Dutch side PSV Eindhoven at the Philips Stadion.
Defender Adil Rami put Valencia ahead early on in the second half, before Ola Toivonen made it all-square on the night in the 64th minute.
Despite having to play the final minutes of the match without their goalscorer Rami -- who was dismissed for an off-the-ball incident -- the Spanish side never relinquished their grip on the tie which was set up by a 4-2 win in the first leg.
Atletico Madrid also ran out comfortable winners against Besiktas in Turkey.
Holding a 3-1 advantage from the first leg, Atletico were soon further ahead thanks to a 24th minute goal from Adrian.
Two late goals from Falcao and Eduardo Salvio earned a comfortable 3-0 win on the night and 6-1 on aggregate.
Germany will have two teams in the hat for the quarterfinal draw.
Schalke overturned a 1-0 first-leg deficit to beat Dutch side FC Twente 4-1 on the night and 4-2 on aggregate, while Hanover thrashed Belgian side Standard Liege 4-0 in the second leg of their last-16 tie to win 6-2 on aggregate.
Serie A won't have a representative in the last eight despite a 2-1 victory for Udinese against Dutch team AZ Alkmaar on Thursday night.
Attempting to overturn a 2-0 deficit from the first leg, Udinese started brightly at the Stadio Friuli leveling the tie with two early goals from Italy striker Antonio Di Natale.
But a crucial away goal from Erik Falkenburg in the 31st minute ensured his team progress 3-2 on aggregate.
Two late goals for Ukraine's Metalist Kharkiv ensured they progress to the last eight on away goals at the expense of Greek side Olympiakos.
Carrying a 1-0 advantage into the second leg, the Greeks looked to be in complete control when Ivan Marcano headed home after 15 minutes, but two crucial away goals for the visitors in the final ten minutes -- from Cristian Villagra and Marko Devic -- ensured a 2-1 victory on the night.