Late in the game, Freiburg's Lucas Hoeler had a golden opportunity to snatch the victory, but his shot was expertly blocked by Diogo Leite with a timely sliding tackle.
The draw took Freiburg one point ahead of Bayer Leverkusen into fourth spot, while Union Berlin are seventh, just outside the European placings.
The match was the first between the sides since the final matchday of last season, when Union won at home to keep themselves in the top division in the same year they played in the Champions League.
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On Saturday, league leaders Bayern Munich play at promoted St Pauli, while defending champions Leverkusen travel to last-placed Bochum.
(This story has not been edited by staff and is auto-generated from a syndicated feed.)