The decision overrules sheriffs who had decided there was no case to answer for each of the three men.
The men were arrested for shouting racial abuse at three matches in Glasgow involving Rangers, Dundee, Hearts and Celtic.
The cases have been referred back to be dealt with by the sheriffs.
In one case Sheriff Ruth Anderson QC had said: “The conduct complained of took place within the context of a football match. Football matches are not conducted in silence.
The Crown appealed against the sheriffs’ rulings.
Temporary judge Gordon Nicholson QC, who heard the appeals with Lord Johnston and Lord Nimmo Smith, said: “In our view, any conduct which can reasonably be regarded as likely to provoke violence must be regarded as serious.”
He said they “totally” disagreed with the view that there was something special about a football match which reduced the seriousness of things said or done which might amount to a breach of the peace elsewhere.
The judge said: “Given the potential for disturbance at football matches, we consider the opposite is the case.”