Dortmund, who lie second in the Bundesliga with 15 points from six games, had the better chances but could not get something from the game.
Luca Cigarini scored Sevilla's winner on the stroke of halftime to give new coach Gregorio Manzano a winning start.
He blasted home a powerful shot from inside the area after capitalizing on a poor defensive clearance.
Dortmund's hopes of grabbing the equalizer were dealt a blow four minutes after the restart when Marcel Schmelzer was sent off for a second bookable offense.
Jurgen Klopp's side, who missed Egyptian injured striker Mohamed Zidan, wasted a host of clear-cut opportunities to suffer their first Group J defeat.
French side Paris Saint-Germain top the group with maximum six points after claiming an easy 2-0 victory over Ukrainian side Karpaty Lviv.
Dortmund and Sevilla are joint second with three points each.
Dortmund 0-1 Sevilla