Fran Escriba's side went into the match knowing that only a win would delay confirmation of a fate which has looked inevitable for some time, with Elche sitting 17 points adrift of safety with only 18 points left to play for ahead of Tuesday's match.
A shock 4-0 victory over mid-table Rayo Vallecano at the weekend had staved off the threat of relegation for a few days at least, but they were condemned to their 23rd league defeat of the season at Estadio de los Juegos Mediterraneos to officially end their four-year stay in La Liga.
Elche did have chances to put the pressure on their hosts during the first half, but they failed to make the most of those and Leo Baptistao's strike midway through the half ensured that Almeria went into the break with a one-goal lead.
Adri Embarba then doubled the home side's advantage seven minutes into the second half before later hitting the post as Almeria looked to pile more misery on their Segunda Division-bound visitors.
There was a late consolation for Elche through Ezequiel Ponce in the 90th minute, but with nothing less than victory being enough for his side, there was little hope of a remarkable comeback to keep their remote hopes alive.
The result leaves Elche, who have won only three games all season, still 17 points from safety with now only 15 points left on offer.
Almeria, meanwhile, jump from 16th up to 14th and are now five points clear of the relegation zone.
At the other end of the table, Barcelona are now just one win away from claiming the title after they beat Osasuna and Real Madrid were beaten by Real Sociedad.
Barcelona had a man advantage for much of their game against Osasuna at Camp Nou after Jorge Herrando was sent off for bringing down Pedri as the last man.
However, it took until the 85th minute for Xavi's men to make the breakthrough, when Jordi Alba fired home after the ball had broken to him at the back post.
To move within one game of the title, Barcelona still needed help from elsewhere and Real Madrid slumped to their seventh defeat of the season at Champions League-chasing Real Sociedad.
Takefusa Kubo came back to haunt his former club with the opening goal just minutes into the second half, and Madrid's task became even more difficult when Dani Carvajal was shown two yellow cards in the space of eight minutes.
Ander Barrenetxea then sealed the result for the hosts five minutes from time as a Madrid side missing Karim Benzema and Vinicius Junior suffered their second loss in three league games ahead of a big week which seems them face Osasuna in the Copa del Rey final and Manchester City in the Champions League.
The result also leaves Carlo Ancelotti's side 14 points adrift of Barcelona with only 15 points left to play for, meaning that the title could be secured when Madrid next play in the league on May 13, or in Barcelona's next game, which comes at the home of local rivals Espanyol on May 14.