Pierre-Emerick Aubameyang's header seven minutes from time booked 2012 DFB-Pokal winners Borussia Dortmund a place in the final four of this season's competition.
The Gabon international clinched a 1-0 victory for Dortmund over Eintracht Frankfurt - just when a game dominated by Jurgen Klopp's men appeared to be heading for extra time.
They will find out which other three sides will join them in the draw for the semi-finals on Wednesday night, when holders Bayern Munich travel to Hamburg, Hoffenheim host Wolfsburg and Bayer Leverkusen tackle second-tier Kaiserslautern.
With the chances of Bundesliga glory looking slim, given the 17-point deficit on leaders Bayern, the DFB-Pokal could well present Dortmund with their best chance of silverware this term.
With that in mind, they soon built up a head of steam with Robert Lewandowski starting what was to be an intriguing battle with Carlos Zambrano.
The Frankfurt defender's close attention of the Pole helped the hosts keep themselves in the tie while frustrating the Bundesliga's second-highest scorer.
Henrikh Mkhitaryan was guilty of missing the best chances, though, as he exploited the room left open to him, albeit without showing the incision which had helped him score twice against Werder Bremen at the weekend.
Frankfurt also had goalkeeper Kevin Trapp to thank for keeping them in the tie at half-time.
The hosts then carved out a few chances of their own in the second half, but Sebastian Jung first and then Sebastian Rode subsequently failed to deliver the killer ball for Alexander Meier.
As the game appeared to be creeping towards extra time, Dortmund raised the intensity even further and Lewandowski had a penalty appeal turned down.
Mkhitaryan missed another chance he would probably have put away with ease at the weekend before a corner earned them their goal.
It was a training-ground set-piece with Sebastian Kehl peeling away at the near post to flick the ball on to the back post, where Aubameyang only just managed to head in.
It was ultimately a deserved win for the Westphalians, who become the first side to take their place in the DFB-Pokal semi-finals.