The away side had the lead after 23 minutes when Carlos Bacca found the bottom corner, with that strike separating the two sides at the interval.
Granada were level just past the hour mark when Yacine Brahimi converted from the penalty spot. Sevilla regained the lead in the latter stages, however, when Kevin Gameiro found the bottom corner after good work from Bacca.
Read how it all unfolded in Sports Mole's minute-by-minute live commentary of the action below.
GRANADA: Roberto; Foulquier, Murillo, Diakhate, Angulo; Recio, Yebda, Rico, Brahimi, Piti; El Arabi
SEVILLA: Beto; Navarro, Fazio, Carrico, Figueiras; Mbia, Rakitic, Iborra; Reyes, Bacca, Jairo