El Grana lift themselves off the bottom of the table after a stunning recovery sees them record a victory over their Andalusian rivals
Manu del Moral had put Sevilla ahead inside the first minute of the match but a spirited fightback from Granada saw a Alex Geijo goal and Rico's late strike inflict Sevilla's first defeat of the season.
Sevilla took the lead inside the first minute when Granada failed to deal with Jesus Navas' cross ultimately leading to Roberto parrying Frederic Kanoute's shot into the path of Manu del Moral, who crashed the rebound home.
Further chances came the home side's way before the ten minute mark with Manu, Jesus Navas and Piotr Trochowski all squandering good opportunities to double Sevilla's lead.
Meanwhile, Granada's influence grew and it had a good opportunity to level when it was awarded a free kick in a promising position. Abel tested the palms of Javi Varas with the set piece and from the resulting corner a timely intervention from Martin Caceres prevented a tap-in for two lurking Granada players.
Sevilla began to realize that its slender lead was under threat and re-emerged from the break with the intention of finding a second. They nearly managed to pull it off when Emiliano Armenteros was unchallenged five meters from goal but he put his header wide. Roberto was then in fine reactionary form saving from Manu, Armenteros and Jesus Navas all in quick succession to deny Sevilla a second goal.
Granada's best chance came and went when a corner kick was scrambled to Uche just three meters from goal but inexplicably the Nigerian striker scooped his effort over the bar.
Javi Varas was left wrong-footed when Franco Jara's shot hammered off the crossbar and onto the head of Alex Geijo who gratefully nodded home to level the match with little over ten minutes remaining.
Granada then stunned the home faithful with a stunning strike in the 90th minute when Mikel Rico forced a shot home for the edge of the area to send the travelling support into a craze.
Sevilla was left ruing numerous missed chances as Marcelino Toral's side fell further behind Valencia in pursuit of the last Champions League spot as a result of this defeat.
Meanwhile, Granada lifted itself off the bottom of the table with the dramatic late win against its Andalusian rivals and will look ahead to its match against Racing in earnest as it looks to put its season back on track.