Moroccan striker Youssef En-Nesyri, a reported January transfer target for West Ham, turned in a Jesus Navas cross to give Sevilla the lead on three minutes.
Edgar Mendez soon levelled for the hosts but a thunderous 30-yard drive from Suso put Sevilla back in front on the half-hour, with goalkeeper Bono saving a stoppage-time penalty from Joselu to preserve the win.
Julen Lopetegui's side moved up two spots ahead of a favourable run of matches against clubs largely in the bottom half of the table.
Real Valladolid recovered from two goals down to draw 2-2 at home to Elche while Cadiz and Levante also ended two apiece.
Leader Atletico Madrid can extend its cushion at the top when it visits Eibar on Friday (AEDT). Diego Simeone's side is four points clear of Real Madrid with two games in hand.