Duisburg, who played the most recent of their three losing Cup finals in 1998, could win a Europa League spot if holders Bayern Munich win their semi-final against Schalke 04 on Wednesday and finish in the top three in the league.
The 2.Bundesliga side were lucky to take the lead on 24 minutes when Cottbus defender Uwe Huenemeier attempted to clear a cross in the box but his header deflected off Duisburg's Stefan Maierhofer into the net.
There was nothing lucky about the Zebras' second goal when they executed a textbook quick break down the right, beating the offside trap and cutting back for Srdjan Baljak to tap in from close range.
The 32-year-old Serbian then turned provider a little later as Cottbus poured forward, floating a cross for Olcay Sahan but his powerful header rattled the crossbar.
Cottbus, who had hoped for a second cup final appearance after losing in 1997, pulled one back 12 minutes from time when Nils Petersen converted a spot-kick with Duisburg left with 10 men after Bruno Soares was sent off for pulling down Jules Reimerink.
The visitors poured forward and went close to an equaliser in the last minute when Huenemeier's header was first cleared off the line and Jiayi Shao's follow-up struck the post.
