Sevilla took a lead after just three minutes as Ever Banega scored from a free kick.
But two goals from Lionel Messi and one apiece from Rafinha and Luis Suarez took Barcelona into a seemingly-insurmountable 4-1 lead.
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Sevilla had other ideas, however, with José Antonio Reyes and Kevin Gameiro pulling goals back.
And when Jeremy Mathieu conceded a penalty with 10 minutes left, sub Yevgen Konoplyanka stepped up to level from the spot.
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