Celta Vigo and Getafe both lost to third-tier teams in the Copa del Rey's round of 32 while Real Valladolid only just survived a similar fate.
Celta were humbled 5-2 at Ibiza in a match played on artificial turf on the Balearic Island.
The visitors fell behind 3-0 within the first half hour as Ibiza's Sergio Castel scored twice and Javi Perez added a third.
Manu Molina increased the margin from the penalty spot before Celta's Santi Mina and Jordan Holsgrove pulled two goals back.
Angel Rodado completed the memorable rout for the minnows in stoppage time.
Celta, who are in eighth place in the Spanish top flight, were playing without several regular starters, including injured forwards Iago Apsas and Manuel "Nolito" Agudo.
Ibiza are undefeated and lead their third-division group with six wins and two draws.
"The excitement of our fans pushed us to this victory," Ibiza coach Juan Carlos Carcedo said.
Getafe's poor run in the league was compounded by a 1-0 defeat at Cordoba.
Striker Willy Ledesma struck for Cordoba in the seventh minute.
The visitors were unable to respond despite having striker Angel Rodriguez leading its attack and putting Juan Mata on for the final 35 minutes.
Getafe have only one win in the past 11 rounds in La Liga to be 16th while Cordoba are in second place in their group in the third tier.
"Now is the moment to be calm and for reflection," said Jose Bordalas, whose Getafe are going through their worst stretch with him as coach.
"We are all angry, and as of tomorrow we will focus on La Liga."
Meanwhile, a trio of top-flight clubs reached the last 16 as Sevilla won 2-0 at Linares, Villarreal accounted for Zamora 4-1 and Real Valladolid edged third-tier Marbella 3-2 in extra time.
In Tuesday evening's other game, Alcorcon defeated Real Zaragoza 2-1 in a battle of Segunda Division sides.