The visitors went ahead through Angel Correa but El Bilal Toure pegged back Diego Simeone's side, fourth and 13 points behind leaders Barcelona.
Atletico should have won the game in the second half but Almeria goalkeeper Fernando Martinez made stunning saves to deny Alvaro Morata and Correa.
Sergio Reguilon, who came on as a substitute, was sent off for Atletico for two yellow cards in under five minutes in the final stages.
Simeone's side have now won just one of their last six league games, against bottom-of-the-table Elche.
Atletico had taken the lead in the 18th minute after a clever dummy by Antoine Griezmann allowed Correa to run on to Geoffrey Kondogbia's pass.
The Argentine fired home at the near post to record his 50th league goal for the Rojiblancos.
Sergio Akieme lashed over as Almeria searched for an instant response, more than holding their own in the first half.
Eventually, the hosts levelled before the break through Toure, netting his fourth league goal of the season with a powerful header from Lucas Robertone's cross.
The Mali international found space behind Axel Witsel and capitalised brilliantly.
Robertone continued to prove a thorn in Atletico's side in the second half, playing a fine ball to Colombian striker Luis Suarez, who sent an effort wide.
Atletico substitute Morata should have levelled at the end of a swift counter but Almeria goalkeeper Fernando clawed out his effort and then pushed the loose ball to safety.
The stopper then produced another sublime save with his leg to deny Correa from point-blank range.
Fernando's saves saw his team move three points clear of the relegation zone, up to 13th.
Earlier Espanyol won 2-1 at Getafe, with striker Joselu scoring from around 40 yards out.
The forward lobbed David Soria in the sixth minute to break the deadlock, but Enes Unal equalised with a superb effort of his own from a wide position on the left.
Javi Puado won the game for the visitors with a fine solo dribble and finish in the second half, helping Espanyol climb to 14th, level on points with opponents Getafe, 15th.
Espanyol's win means Sevilla drop provisionally to 18th after their defeat at Girona on Saturday.