The home side started the match the stronger and Mikel Rico might have scored with a header after just two minutes, but it drifted wide.
Rico again came close for the home side after 33 minutes, but once more he headed wide when he might have done better.
Sevilla took the lead after 39 minutes courtesy of Negredo, who finished coolly in the box after a searching ball from Reyes.
Sevilla moved 2-0 ahead after 54 minutes when Manu del Moral found the bottom corner after good work from Negredo.
Del Moral might have added his second of the night with a header moments later, but he fired wide.
Chances were few and far between as the match progressed, with Sevilla always comfortable protecting their lead.
Del Moral added a third for the away side in the final minute, to secure a welcome three points.
Sevilla have moved into ninth while Granada remain 17th.