After a strong start Union, who set a club record with their 21st straight unbeaten home league game, were on the back foot.
"We are satisfied because it was an intense game," said Union coach Urs Fischer, whose team are having their best ever Bundesliga season.
"We wanted to try and win the game but then we had to stay sensible towards the end."
"Both teams had their chances so for me it was a great 0-0," added the Swiss coach.
The result benefited neither team with Union remaining third but Freiburg joining them on 56 points -- a club record -- after their 1-0 win at Cologne.
RB Leipzig, in fifth on 54, also moved within striking distance following their 1-0 home victory over Hoffenheim.
Leverkusen, who visit AS Roma in a Europa League semifinal first leg on May 11, stretched their unbeaten run to 14 matches in all competitions but stayed sixth on 48 points.
- Marco Fritz
|1. FC Heidenheim 1846||13||3||2||8||-10||11|
|SV Darmstadt 98||13||2||3||8||-19||9|
|1. FC Union Berlin||12||2||1||9||-15||7|