"We were well beaten. They were the better team,'' United manager Alex Ferguson said.
Bilbao has been rejuvenated under veteran Argentine coach Marcelo Bielsa and with the emergence of a golden crop of youngsters. The team was expected to give United a tough game after climbing to fifth place in the Spanish league, but no one could have expected such domination from the away side.
A handful in attack all night, Llorente stooped to head the equaliser in the 44th minute to cancel out Rooney's close-range opener.
Bilbao poured forward with wave after wave of attacks, United goalkeeper David De Gea denying Llorente twice and then Muniain. De Marcos, however, finished a classy move full of one-touch passing by volleying home a scooped pass by Ander Herrera.
Muniain capitalized on hesitant defending by Rafael to slam home the third from close range, sealing back-to-back home losses for United in Europe for the first time in 16 years. United was defeated 2-1 by Ajax in the last 32.
Rooney's penalty, given for handball against De Marcos, gave United something to cling to for the second leg at San Mames stadium next week.
"We can win the game over there,'' Ferguson said. "We've shown we can create chances, but we will need to defend better.''
Like its fierce local rival, City also dropped into Europe's second-tier competition after finishing third in its Champions league group. But having dispatched reigning champion FC Porto with ease in the last 32, City came unstuck against another Portuguese team.
It took a moment of class to settle the game, Xandao pouncing in the 51st minute after City goalkeeper Joe Hart had failed to palm Matias Fernandez's free kick to safety.
Mario Balotelli, on as a substitute, hit the crossbar with a header as City rallied late on.
"I'm not worried. We will go through,'' City manager Roberto Mancini said. "It wasn't a surprise because anything can happen in football, but I don't think we deserved to lose.''
City's misery was compounded by an injury to captain Vincent Kompany, who limped off with a calf injury after seven minutes.
Fresh off a hat trick for Spain in a friendly against Venezuela last week, Roberto Soldado scored twice for Valencia. Victor Ruiz and Pablo Piatti helped put the Spaniards 4-0 up at the Mestalla.
Goals in the final seven minutes by Ola Toivonen and Georginio Wijnaldum reduced the deficit for PSV, a former European champion.
Atletico, winner of the competition in 2010, will take a healthy cushion into the second leg against Besiktas after a superb first-half showing at Vicente Calderon stadium.
Argentina winger Eduardo Silvio scored in the 24th and 27th minutes, and Adrian Lopez made it 3-0 with a stunning individual effort eight minutes before halftime.
Besiktas will take a glimmer of hope into the return leg thanks to a powerful strike by Portuguese winger Simao Sabrosa, who started the 2010 final for Atletico.
Dutch side FC Twente beat 2011 Champions League semifinalist Schalke 1-0 from Luuk de Jong's second-half goal. David Fuster's 50th-minute goal earned Olympiakos a 1-0 win at Metalist Kharkiv, which had Edmar sent off eight minutes from time.
Standard Liege drew 2-2 at home to Hannover and AZ Alkmaar scored two second-half goals to beat Udinese 2-0 at home.
-AP
