Freiburg started the stronger side and took the lead through Maximilian Eggestein, who reacted quickest to turn home from close range after a dangerous set-piece. The visitors looked confident and held their advantage going into the break, while Stuttgart struggled to register a shot on target despite several half chances.
After the restart, Stuttgart increased the pressure. Deniz Undav eventually brought them level with a composed first-time finish following a swift counter-attack. Freiburg goalkeeper Florian Muller made a string of key saves to keep his side in the contest, denying Stuttgart repeatedly as the match swung in the hosts' favour.
The game moved into extra time, where Stuttgart continued to dominate. With penalties looming, Tiago Tomas delivered the decisive moment, timing his run perfectly to flick home a low cross and send Stuttgart into the final.
Head coach Sebastian Hoeness praised his team's persistence after the match. "I'm super happy," he said. "It was a difficult game for us. We needed something to get going, but the equaliser was deserved based on our chances."
Reflecting on the winner, he added: "It was a mad goal. What a moment to send us to Berlin. I don't have the words. Tiago did it brilliantly, but I also feel for Freiburg - they've had an outstanding season."
Hoeness admitted relief at avoiding penalties. "There was a feeling it might not be our day, but I'm very happy we didn't need a shootout. For my nerves, that was very good."
Stuttgart's victory extended their remarkable cup run and booked a final against Bayern Munich. "We know what's waiting for us," Hoeness said. "But I'm looking forward to it. We'll give everything."