The game started at a frantic pace in the opening five minutes, with the referee called into action after a number of late challenges in midfield.
The home side began to force the issue and had the first chance of the game on eight minutes after Carles Gil was brought down on the edge of the area. However, Cristian Herrera could only clip the ball wide from the resulting set piece.
Herrera had a wonderful chance to give his side the lead on 15 minutes, but after breaking clear from the defence, the Spaniard could only fire straight at the goalkeeper.
Gil had another effort for Elche five minutes later, but his strike towards the top corner flew just over the bar.
David Lomban should have gave the hosts the lead on 33 minutes, but his close-range header from a corner went over the crossbar.
Almeria's best chance came just before the half-time whistle when Verza found some space on the edge of the box, however, his strike was saved.
The away team started the second half well and almost grabbed the lead on 53 minutes when Jonathan Zongo found himself unmarked at the back post, but his effort was blazed over the bar.
Elche finally broke the deadlock on 58 minutes through Javier Marquez, whose long-range strike went in with the aid of a deflection.
Almeria began to push forward in search of an equaliser and came close when Zongo directed a header towards the bottom corner, but the goalkeeper kept out the forward's effort.
As the game drew to a close, it became heated between the two sides, resulting in a second yellow for Damian Suarez for a late challenge on 90 minutes.
However, despite going down to ten men, Elche held on to secure all three points.