Joaquin Caparros' side were not content with their lead and spent most of the second half looking for another goal, finally getting it through midfielder Sarabia's cool low finish after being picked out by striker Wissam Ben Yedder.
The win took Sevilla up to sixth on 46 points, level with Valencia and one point behind Getafe who occupy the final Champions League spot with eight games left.
Alaves would have gone level on points with Getafe with a victory but instead slid to seventh and remain on 44.
(Reporting by Richard Martin; Editing by Ken Ferris)
