Diego Costa's double got Diego Simeone's men off to an ideal start in La Liga in 2012-13 as Granada claimed a 2-1 away win over Osasuna
In a feisty encounter, which saw a total of nine players pick up a booking, Diego Costa opened the scoring on 35 minutes, but the capital club were soon pegged back, with Diego Perotti equalising minutes later.
Sevilla had enjoyed the lion's share of possession but Costa, courted this summer by Liverpool, looked to have sealed all three points just over 10 minutes from time.
And, to put the result beyond all doubt, Cristian Rodriguez made it 3-1 in stoppage time to seal all three points once and for all.
Meanwhile, Granada warmed up for their clash with Real Madrid next week with a 2-1 victory against Osasuna at Pamplona.
Youssef El Arabi opened the scoring seven minutes from the break, and Hassan Yebda ensured the Andalusians had a handsome lead at the break with a stoppage time goal.
Patxi Punal pulled one back for the hosts on 58 minutes, but Lucas Alcaraz's side were able to hold on and claim all three points.
In Sunday's other action, debutant Isco struck late on to ensure Real Madrid claimed a 2-1 home win over Betis in Carlo Ancelotti's first game in charge, while a Cesc Fabregas-inspired Barcelona dismantled Levante 7-0 at Camp Nou.