Police were forced to restrain supporters who broke through a fence, with fans clearly enraged by their team’s collapse.
A section of Dortmund fans also attempted to reach their Schalke counterparts, only to be repelled by the police.
Goals from Pierre-Emerick Aubameyang, who was later sent off, Mario Gotze and Raphael Guerreiro, plus a Benjamin Stambouli own goal, gave Dortmund a seemingly unassailable lead at half-time.
However, their fierce rivals fought back in the second half, with Guido Burgstaller, Amine Harit and Daniel Caligiuri giving Schalke hope of a miraculous comeback, before Naldo amazingly levelled proceedings in injury time.
The result will crank up the pressure on Dortmund manager Peter Bosz, whose side's only win in any competition since the end of September came when they defeated FC Magdeburg, of the German third division, in the DFB Cup last month.
The club are nevertheless fourth in the Bundesliga, eight points behind leaders Bayern Munich, who have a game in hand.