It was, however, the visitors that missed the opening chance of the first half through Adnan Januzaj, who after a nice run produced a tame finish that was easily gathered by Orjan Nyland.
Albert Sambi Lokonga then had two decent opportunities for Sevilla, the first of which he struck over, before forcing Dinko Horkas to palm away his second effort.
Jose Campana tried his luck from range at the other end, but again Nyland easily saved as it remained goalless at half-time.
It did not take long for the deadlock to be broken in the second half though, as Lucien Agoume flicked on a free-kick towards Alvaro Garcia Pascual, who picked a great time to score his first Sevilla goal by heading into the bottom corner.
Las Palmas did not offer much in response, and it was the hosts that were close to doubling their lead when Suso’s dangerous free-kick had to be punched away by Horkas.
Nonetheless, the visitors did have the ball in the net in the latter stages as Oli McBurnie thought he tapped in an equaliser, but Sergi Cardona was adjudged to have fouled Nyland beforehand.
In the end, Las Palmas lost an eighth head-to-head in nine against Sevilla, and a fourth straight league defeat means they remain in 19th and three points from safety with just two games to play.
The hosts rise to 14th with victory, and have all but confirmed survival as a result.
Flashscore Man of the Match: Alvaro Garcia Pascual (Sevilla)
