Sevilla's first chance came through on-loan Queens Park Rangers midfielder Stephane Mbia, who rose highest in the box but then placed his header wide.
Celta came even closer, however, when Santi Mina smashed his shot against the post.
Beto then came to collect a dangerous cross as the away side continued their good spell.
Mina had a great chance just before the break, but his shot was blocked at the crucial moment.
Just three minutes into the second half Celta were in front as Beto presented the ball to Alex Lopez who slotted in.
Mbia then showed his prowess in the air, directing a header against the post. However, Celta showed their quality on the counter-attack with Fernandez going close.
Kevin Gameiro appealed for a late penalty after going down in the box, but the referee disagreed.