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 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.
