Penalties were looming in Monday's tie between second-tier side Greuther Furth and Bundesliga giant Dortmund.
But Reus slammed home a low right-wing cross from Jadon Sancho to ensure Lucien Favre's men progressed with a 2-1 victory after extra time.
Dortmund fell behind in the 77th minute, with Sebastian Ernst on target for the host, but Dortmund dramatically forced extra-time.
Axel Witsel's first goal for the club came in the 95th minute, the Belgium midfielder volleying in from close range as Dortmund left it late to level.
And Dortmund captain Reus came up with the decisive goal to break Greuther Furth hearts and prevent Dortmund from following holder Eintracht Frankfurt out.