Las Palmas got a stoppage-time winner after Eibar had two players sent off to secure a 3-2 away win in the Copa del Rey on Thursday.
Jeronimo "Momo" Figueroa curled the ball just inside the post to grab the win, after Las Palmas had erased two one-goal deficits en route to their first away victory of the season.
Izet Hajrovic opened the scoring for Eibar in the 10th minute, only for the visitors to equalise six minutes later with Aythami's goal.
But on 20 minutes Eibar were again on top through Saul Berjon.
Wakaso Mubarak brought Las Palmas back level again on the hour mark before things really fell apart for Eibar.
Eibar's Izet Hajrovic and substitute Gonzalo Escalante both earned straight red cards for violent tackles in the final 10 minutes.
Cadiz advanced to the round of 16 after previous opponent Real Madrid was disqualified for fielding an ineligible player, but the third-tier team will have to overcome a 3-0 home defeat to Celta Vigo to go any further.
John Guidetti scored twice in the second half, either side of Johny's goal, as the Primera Division side took a large advantage.