Augsburg failed to take advantage of Fortuna Dusseldorf's defeat to Eintracht Frankfurt on Saturday as they remained in the bottom three of the Bundesliga with two games of the season remaining after going down 2-0 to Freiburg.
Cedrick Makiadi's and Jonathan Schmid's goals were enough to get Freiburg back to winning ways after two defeats and allow them to consolidate their sixth position and consequent berth in the Europa League next season.
Hamburg missed the chance to significantly enhance their own hopes after letting a lead slip in a 1-1 draw at home to Wolfsburg.
Heiko Westermann nodded Hamburg into a half-time lead but the visitors extended their unbeaten run to eight games thanks to Makoto Hasebe's leveller.
The result means Hamburg are three points behind sixth-placed Freiburg, who, as it stands, occupy the final Europa League spot. Freiburg also have a vastly superior goal difference with just two games to go.
Information from the Press Association was used in this report