The visitors had the first chance of the game, but Adnan Januzaj's shot was easily saved by Orjan Nyland. Albert Sambi Lokonga then had two opportunities for Sevilla, but his first shot went over the bar and his second was blocked by Dinko Horkas.
Jose Campana tried his luck from distance, but Nyland saved the shot again. The score remained 0-0 at halftime.
The deadlock was broken in the second half when Lucien Agoume played a free-kick to Alvaro Garcia Pascual, who scored his first goal for Sevilla with a headed finish into the bottom corner.
Las Palmas did not create many chances in response, and Sevilla were close to doubling their lead when Suso's free-kick was punched away by Horkas. In the late stages, Oli McBurnie thought he had equalized, but the goal was ruled out due to a foul on Sergi Cardona.
Las Palmas lost their eighth head-to-head match against Sevilla in nine attempts and suffered a fourth consecutive league defeat, leaving them in 19th place and three points from safety with two games remaining.
Sevilla, on the other hand, rose to 14th place with the win and have effectively secured their survival in the league.
Flashscore Man of the Match: Alvaro Garcia Pascual (Sevilla)