A jury had acquitted them on most of 11 charges involving drug prescriptions given to the former Playboy model in the months before she died of an accidental drug overdose in February 2007.
The judge dismissed the conspiracy counts against Howard K. Stern and Dr. Khristine Eroshevich, saying they were trying to protect Smith's name as a celebrity.
The judge reduced the one conviction against Eroshevich - obtaining Vicodin under a false name - to a misdemeanor.
A co-defendant, Dr. Sandeep Kapoor, who was Smith's physician, was acquitted of all charges.
Prosecutors said the judge was biased against them and had created a celebrity exception to the law.
"Having repeatedly and unequivocally expressed its bias against this case and the trial prosecutors," the appeal said, "the court granted the new trial motions and dismissed the case, not because substantial evidence was lacking to support the verdicts ... but rather, because the court wanted to usurp the charging power of the People."
The Associated Press contributed to this report.