Real Madrid youth product Pablo Sarabia produced a great piece of skill to make space for a 35th-minute shot that was saved by Las Palmas goalkeeper Leandro Chichizola, and Wissam Ben Yedder netted the loose ball to put Sevilla ahead.
Sarabia then turned in a cross by languid Argentine Franco Vazquez to double Sevillas lead five minutes into the second half in Gran Canaria.
However, Jonathan Calleri pulled one back for Las Palmas from the penalty spot after Alen Halilovic had been fouled by Miguel Layun, the Mexican former Watford full-back.
Having experienced some indifferent form following the appointment of Italian Vincenzo Montella at the end of December, Sevilla have now claimed back-to-back league victories since progressing to the Copa del Rey final, in which they will play Barcelona.
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They are provisionally fifth in the table, three points behind Real Madrid in fourth but having played two games more.
Sevilla host Jose Mourinhos United in the first leg of their Champions League last-16 tie at the Ramon Sanchez Pizjuan on Wednesday.
Leaders Barcelona are hoping to continue their unbeaten record in La Liga this season when they face Eibar later, with Real and second-placed Atletico Madrid both in action on Sunday.
Atletico host Athletic Bilbao, while Zinedine Zidanes Real are at Betis.