Zaragoza are currently playing consecutive seasons in the second tier of Spanish football for the first time since 1956 after they struggled to 14th last term.
And their poor start to the current season continued as their winless streak extended to four matches courtesy of Chumbi's goal on the stroke of half-time.
Albacete – who also play in Segunda Division – had not won this season either prior to their triumph at the Estadio Carlos Belmonte.
Javier Matilla broke the deadlock for Betis – relegated from La Liga last term – in the 46th minute before Vincenzo Rennella doubled their lead nine minutes later.
Mirandes' class told with a 4-1 win over Racing Ferrol. The second-tier side beat their Segunda B opponents comfortably thanks to a hat-trick from Urko Vera, while Las Palmas won 2-0 at Mallorca.
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.
