
The match finished goalless in regular time before Hee-Chan Hwang fired Leipzig ahead in the 93rd minute with a clinical finish from 8m after the home team’s defence failed to clear the danger.
Bremen, who were on the back foot throughout the contest, levelled in the 105th minute when Leonardo Bittencourt took advantage of Dayot Upamecano’s error and steered the ball home after rounding goalkeeper Peter Gulacsi.
With a penalty shootout looming, Forsberg popped up to volley home superbly with almost the last kick of the game after Hwang headed a Kevin Kampl cross from the right into the Swedish forward’s path.
Borussia Dortmund are at home to second-tier side Holstein Kiel in the other semifinal on Saturday.