"I am pleased that we keep the points," said Bayern coach Julian Nagelsmann.
His team had an extra man on the pitch for 18 seconds late in last Saturday's 4-1 away win after two players came on, but only one came off, leading Freiburg to lodge an appeal on Monday.
However on Friday, the sports court of the German Football Association (DFB) blamed the mix up on the match officials.
"The minor contribution of fault by Bayern... takes a back seat to the misconduct of the referees," said Stephan Oberholz, chairman of the DFB's sports court.
"It is not sufficient enough to justify the serious legal consequence of a match reclassification" and the three points being awarded to Freiburg.
The decision means Bayern retain their nine-point lead in the table and look set for a tenth straight Bundesliga title.
Freiburg were clearly uncomfortable with having to lodge a protest and in a statement last Monday, the club described the situation as a "dilemma through no fault of our own".
Freiburg coach Christian Streich had stressed that the appeal "wasn't about us getting the points".
However, the club from Germany's Black Forest are just three points from the lucrative Champions League places for next season.
On Tuesday, Nagelsmann had slammed Freiburg's senior bosses for appealing, but he walked back his comments on Friday.
"I want to emphasise that I am in no way disappointed in Christian Streich or (Freiburg sports director) Jochen Saier," Nagelsmann said.
"I only expressed my opinion. Christian Streich is an outstanding bloke and coach."