The Spanish side joined PAOK Salonika and Napoli, who left it late to score the goal they needed, in securing three of the remaining berths in the knockout round ahead of Thursday's final day of group matches.
Dortmund, who have a massive 11-point lead at the top of the Bundesliga and needed a win in Spain to progress, had looked on course for the next round when they took a fourth-minute lead through Japanese midfielder Shinji Kagawa.
Two goals in four minutes just after the half hour put the hosts ahead thanks to Ndri Romaric and Frederic Kanoute. Dortmund levelled through Neven Subotic's header on 49 minutes. Sevilla were runners-up to Paris St Germain in Group J.
Napoli waited until the third minute of stoppage time for the goal they needed to beat Steaua Bucharest 1-0 and qualify at the expense of the Romanians in Group K, won by Liverpool.
Edinson Cavani nodded in at the near post to make sure there would be one Italian representative in the next round.
In another game where both teams were chasing a qualifying berth, PAOK Salonika won 1-0 at Dinamo Zagreb to take the second Group D spot behind Villarreal thanks to Dimitris Salpingidis' strike on the hour.
Group F winners CSKA Moscow's perfect record came to an end after they drew 1-1 away to Sparta Prague, who had also already qualified.