The Europa League winners had taken a 13th-minute lead thanks to Lucas Ocampos' calmly taken penalty, only for Leon Goretzka's well-taken goal to bring Bayern level 11 minutes before the break.
However, despite having two goals disallowed, the European champions eventually found a way past Sevilla goalkeeper Yassine Bono thanks to substitute Javi Martinez's header in extra time.
But Hansi Flick's side may have headed into Thursday night's clash in Budapest having won their last 22 games in a row, because it was the Spaniards who went ahead just before the quarter-hour mark when eagled-eyed English official Anthony Taylor spotted that Ivan Rakitic had been pulled back by David Alaba while trying to latch on to Luuk de Jong's clever headed knock down.