Alvaro Negredo, whose penalty kick won the game for Sevilla, dedicated the goal to teammate Sergio Sanchez, whose career is probably over after he was diagnosed with a heart condition.
Barca lost despite having Lionel Messi in the lineup for the first time after being away for an extended Christmas break.
It was without Malian Seydou Keita and Ivorian Toure Yaya, who have left for the Africa Cup of Nations.
The loss immediately started talk about Barca's dominance being over.
"I think it's a little early to start talking about an end of an era," outgoing Barcelona president Joan Laporta, "but everyone is entitled to his opinions."