The La Liga pair joined Atletico Madrid in being humbled by lower league opposition after Quique Sanchez Flores's side had Tomas Ujfalusi sent off on Wednesday as they were thumped 3-0 at second-tier strugglers Recreativo Huelva.
Mallorca, fourth in Spain's top flight, failed to reproduce their impressive league form at Rayo's snowy Teresa Rivero stadium in Madrid and went behind after a quarter of an hour.
Michel burst through the centre, rounded goalkeeper German Lux and calmly slotted the ball into the empty net.
Mallorca midfielder Julio Alvarez netted a precise shot five minutes later but the visitors were rocked when defender Felipe Mattioni was shown a second yellow card for shirt pulling.
Juan Jose Collantes headed in from a tight angle to restore Rayo's lead two minutes before halftime and Mallorca had a lucky escape late on when defender Enrique Corrales cleared a shot off the line.
Hercules took the lead in Alicante after 17 minutes when Cristian swept the ball past Osasuna goalkeeper Roberto Fernandez to complete a fine passing move.
Striker Jorge Galan levelled shortly after the break before Joseba del Olmo smashed the winner in off the bar with just over 20 minutes remaining to give the second division leaders the advantage ahead of next week's second leg in Pamplona.
SWERVING FREEKICK
In Thursday's other first leg, relegation-threatened Malaga beat visiting Getafe 2-1 in an all-La Liga clash at a half-empty Rosaleda stadium.
Apono surprised Getafe keeper Jordi Codina with a shot from distance that went in off a post after nine minutes and Edinho's wickedly swerving freekick doubled the home side's lead a minute before the break.
Getafe were gifted a potentially valuable away goal with 23 minutes remaining when Malaga's Milan Stepanov attempted a clearance that looped over his own keeper Roberto Santamaria.
Holders Barcelona slipped to a 2-1 home defeat by 2007 winners Sevilla in their first leg at the Nou Camp on Tuesday.
In Wednesday's other matches, Deportivo La Coruna snatched a 2-1 win at La Liga rivals Valencia, and Villarreal drew 1-1 at second division Celta Vigo.
Third-tier Alcorcon, who dumped Real Madrid out in the last round, fell 3-1 behind at home to Racing Santander but netted a late goal to keep alive their hopes of causing another upset.
The return legs are next Tuesday, Wednesday and Thursday.
‘Arteta, Alonso, Emery, me… none of us were physical players – we needed the understanding of the game. That probably helped us move into management’: Premier League boss reveals reasons for natural career progression
‘England have the players to win the World Cup – it’ll be tough for Thomas Tuchel to do a bad job, with the squad he has at his disposal’ Former Three Lions winger backs new boss after gentle qualifying draw
