Six-time Copa del Rey winner Real Zaragoza suffered a second-round exit at the hands of Albacete on Thursday (AEST).
Zaragoza is currently playing consecutive seasons in the second tier of Spanish football for the first time since 1956 after struggling to 14th last term.
And its poor start to the current season continued as its winless streak extended to four matches courtesy of Chumbi's goal on the stroke of half-time.
Albacete – which also plays in Segunda Division – had not won this season either prior to its triumph at Estadio Carlos Belmonte.
Zaragoza last won the Copa del Rey in 2004, defeating Real Madrid 3-2 after extra time.
Real Betis avoided an upset with a 2-0 home triumph against Llagostera.
Javier Matilla broke the deadlock for Betis – relegated from La Liga last term – in the 46th minute before Vincenzo Rennella doubled the lead nine minutes later.
Another team which lost its top-flight status earlier this year, Real Valladolid, was a 3-1 winner at Sporting Gijon.
Alejandro Alfaro and Samuel Llorca both netted in the second half for Valladolid.
Mirandes's class told with a 4-1 win over Racing Ferrol. The second-tier side beat its Segunda B opponent comfortably thanks to a hat-trick from Urko Vera, while Las Palmas won 2-0 at Mallorca.
Tercera Division outfit Izarra caused a minor upset with a 3-1 win over third-tier Somozas after extra time.
A host of ties were played between Segunda B sides with Lleida Esportiu thrashing Guadalajara 3-0.
Barakaldo, Alcoyano and L'Hospitalet notched 1-0 wins over Real Aviles, Gimnastic Tarragona and Guijuelo respectively.
Linense cruised to a 4-1 success against Fuenlabrada, Cornella edged Zamora 3-2 and Huesca beat Villanovense on penalties 4-3 after the sides were locked at 2-2 after 120 minutes.
Elsewhere, Cadiz and Recreativo Huelva beat Lealtad and Ponferradina 2-1 and Sabadell won at Real Murcia by the same scoreline.
Murcia edged Eldense 3-2 on penalties after the sides could not be separated at the end of extra time with the score at 1-1.
Numancia also won a penalty shootout against Leganes.
And Leioa of the third tier posted an expected 2-0 win against Teruel of the Tercera Division.