Atletico twice led through Sergio Aguero, but were pegged back on each occasion by goals from Albert Crusat and Henok Goitom.
Quique Sanchez Flores' side had been impressive as they beat Villarreal 3-1 last weekend.
That was the club's finest result for some time in what has been a disappointing league campaign, and they began the day just two points behind sixth-placed Espanyol.
But they started on the back foot in this match and had David de Gea to thank for three fine saves in the opening half an hour.
The Atletico goalkeeper twice made telling interventions to deny Crusat efforts and later produced a fine reaction save to keep out a fierce Leonardo Ulloa shot.
Then, against the run of play, Atletico took the lead.
Tiago pounced on a Crusat error and chipped a clever ball forward to Aguero, who got past Diego Alves and slotted the ball into the empty net.
Almeria deservedly levelled three minutes into the second half when Crusat volleyed Luis Perea's poor clearance into the corner from 16 yards.
Aguero then advanced into the area and slotted a low left-footed drive into the bottom corner to make it 2-1 on the hour, but Atletico were once again unable to hold on to their advantage as Goitom headed home from seven yards with 13 minutes remaining.
There were chances for both sides after that.
Jose Ortiz Bernal and Goitom missed good opportunities for Almeria, while Aguero and Jose Antonio Reyes both came close for Atletico in the closing minutes.