The all-Segunda B clash at Hercules' Estadio Jose Rico Perez saw the visitors twice come from behind - once inside 90 minutes, and again in extra-time.
Ivan Buigues equalised for Eldense in the 118th minute, before they went on to win the shootout 4-3.
Other Segunda B outfits Cadiz and Real Oviedo were comfortable winners over their second-tier rivals.
Cadiz won 3-0 away at San Roque de Lepe, with Juan Villar, Miguel Garcia and Tomas Sanchez all netting.
Sergio Garcia scored a brace for Real Oviedo, as they coasted past SD Amorebieta 4-0.
In one of the more astounding score-lines, seven-man Villanovense advanced past La Hoya Lorca in a shootout 3-1, after extra-time ended 2-2.
Villanovense equalised in regulation time with nine men, but frustrations boiled over again late in the extra half-hour - as they saw another two men dismissed.
Despite their significant numerical disadvantage, they won 3-1 in the shootout.
Second-tier Somozas were 3-0 winners over fourth-tier Varea.
Ander Vitoria scored the only goal as Leioa overcame Sestao 1-0 in an all-second tier encounter, while fourth-tier Izarra edged league rivals Atletico Granadilla 1-0 after extra-time.
Another all Tercera Division encounter saw Teruel thrash Puertollano 3-0 away.
Barakaldo beat Trival Valderas 3-0 to send their Segunda B rivals packing from the tournament, while Huesca edged Toledo 2-1 after 120 minutes.
Lealtad won 2-1 away at Gimnastica Torrelavega, Racing Ferrol were convincing 5-1 winners at home to Atletico Astorga, UCAM Murcia had a 1-0 road win at Cartagena and Linense also won away at Marbella 1-0.
Alcoyano won a shootout 9-8 over Pena Deportiva after normal and extra-time ended 1-1, while Gimnastic Tarragona also advanced after a shootout against Atletico Baleares after a goalless 120 minutes.
Real Aviles and Marino Luanco also played out a goalless contest, before Real advanced on penalties, as did Cornella over Jaen after neither side broke through.
