Dortmund, beaten 4-0 away to Bayern Munich in its last match before the international break, was 3-0 down at half-time in Saturday's (AEDT) clash against the league's bottom side.
Streli Mamba struck twice and Gerrit Holtmann was also on target for Steffen Baumgart's side, while Dortmund lost striker Paco Alcacer to injury before the interval.
Dortmund improved after the break, with Jadon Sancho reducing the deficit two minutes after the restart, and Axel Witsel gave the hosts further hope by scoring with six minutes to go.
Sancho then crossed for Reus to nod home the leveller in the second minute of added time to spare Dortmund an embarrassing defeat, although the captain was unimpressed with his side.
"We can never play like that again," he said after Dortmund missed the chance to move up to second place in the table.
"It was an absolutely poor performance and we are ashamed. We apologise to all our fans."
Pressure has been growing on Lucien Favre, whose side came from two goals down to beat Inter Milan in the UEFA Champions League this month, but Reus defended the under-fire Dortmund coach.
"The coach puts us in a great position every time. We're responsible for putting our performance on the pitch, and we do not have to talk about the coach, but about us," the forward said.
"If 80,000 people come here ... we cannot offer that."
Dortmund will be eight points off the top of the table if Borussia Monchengladbach wins at Union Berlin on Sunday (AEDT).