With so much on the line for the hosts, Elche looked to stamp some early authority on the game, with Álvaro Rodríguez denied from close range before Victor Chust rocketed home his first goal for the club on 19 minutes.
Pedro Bigas’ long throw-in was cleared only as far as the former Real Madrid defender on the edge of Getafe’s box, and he launched an unstoppable effort into David Soria’s top corner.
That gave Eder Sarabia’s team a major confidence boost, and their survival push was aided further six minutes before the break when Getafe captain Djené Dakonam was sent off for a late lunge on Germán Valera.
With a man advantage after the restart, Elche battled to extend their lead, with Grady Diangana flashing a low effort wide from a tight angle just before the hour mark.
As Elche were continually unable to find that all-important second goal in the closing stages, the door for a leveller was left open for Jose Bordalás’ visitors.
However, as LaLiga’s second-lowest scorers away from home this season, they were unable to conjure up anything to test Matías Dituro and rescue a point at Estadio Martínez Valero.
Victory for Sarabia’s men moves them up to 42 points ahead of a trip to Girona next weekend, where, if they avoid defeat, that will send the Catalans down.
Despite defeat, Getafe remain inside the top seven, boasting a one-point lead over the chasing pack.
Flashscore Man of the Match: Victor Chust (Elche)