Alaves, the only second division side left in the competition, were inspired by a Ruben Navarro hat-trick as they came from behind to post a home victory that leaves them in with an excellent chance of making the semi-finals.
Barcelona hopes of Cup success in a dismal season faded as Zaragoza claimed a great result in their first outing under new coach Victor Munoz.
The Catalans created plenty of chances but with Patrick Kluivert looking out of touch up front they suffered a sorry defeat.
Kluivert was put through on goal by Ronaldinho after 35 minutes but chose to scuff a pass towards Javier Saviola instead of shooting and the Dutchman was off target with a header a couple of minutes later.
Zaragoza, who had hardly created a scoring opportunity, took the lead in the 74th minute when Goran Drulic's fall in the area under a challenge from Gerard earned them a penalty.
David Villa kept his cool to beat Victor Valdes from the spot twice after the referee ordering the first kick to be retaken because of the encroachment of several players in the area, and Zaragoza held on to claim a valuable win.
Alaves will be even better placed after a classy victory at home to Celta Vigo.
Celta took an early lead when Chilean striker Mauricio Pinilla headed in from a Peter Luccin free kick but Navarro soon got his side back level when he finished off a smart move involving Pablo and Magno.
Navarro made it 2-1 six minutes before the break with a crashing drive but the tie was wide open again in the 49th minute when Pinilla grabbed his second goal of the night.
Alaves wasted little time restoring their lead, with Navarro completing his hat-trick in the 51st minute before Magno struck with a great volley to make it 4-2 two minutes later.
Real Madrid and Sevilla should have few problems making the semi-finals after posting emphatic wins in games played on Wednesday.
Real beat Valencia 3-0 at the Bernabeu with goals from Raul, Ronaldo and Luis Figo, while Sevilla thrashed Atletico Madrid 4-0.