Jonathan Zongo's second-half header was all that separated the two sides as Miguel Moya pulled off many great saves to keep the scoreline respectable.
The win moves Francisco Rodriguez's side out of the danger zone while their opponents remain midtable following a disappointing run of just one win in their last seven Primera Division matches.
Both sides took a few minutes to get going and it was the away side that could have taken an early lead.
Pablo Sarabia was on target with a close-range shot after five minutes of play but Almeria goalkeeper Esteban Suarez managed to pull off a great save to keep the ball out.
Then, just moments later, Aleix Vidal had a chance down at the other end of the pitch before his effort from the edge of the box went wide of the post.
Fernando Soriano was next to have a go at the Getafe goal but his header was comfortably caught by visiting keeper Moya.
Getafe came close with chances from Pedro Leon and Miguel Michel as the first half wore on before Suso had a great chance to break the deadlock for the home side with a shot from the left channel from 20 yards out, but Moya managed to hold them at bay.
It did not take Almeria long to get on the scoresheet after the break as they came out looking for an opener which Zongo netted after 49 minutes.
The 21-year-old managed to get his head onto the end of Liverpool on-loan striker Suso's corner from the right, which Zongo had in the back of the net from close range to put his side in the lead.
Leon had a chance to pull one back for Luis Garcia's side as the game approached the hour mark but his effort from just outside the penalty box sailed past the post.
Suso could have doubled Almeria's lead minutes later with a free-kick from the right before Moya again made it safe.
And Vidal had a late attempt to add another goal for the home side as the match was drawing to a close but Moya managed to tip the Catalonia striker's shot past the post.