John Leathem, 32, will now serve at least 23 years in prison. He had originally been sentenced to a minimum of 27 years in jail.
Leathem stabbed the 15-year-old 61 times after she stopped at his delicatessen in Clydebank, West Dunbartonshire, in March.
Paige's family said there were no words to describe their feelings.
The teenager's body was found in woods in March last year.
Leathem admitted her murder and claimed to have "panicked" after Paige threatened to report him for sexual assault after she applied for a job.
His car was filmed on CCTV at the site where her body was dumped - a wooded area close to Glasgow's Great Western Road, less than a mile from the deli.
Lawyers for Leatham told the court that he had no previous convictions and had shown genuine remorse.
His original life sentence, with a minimum term of 27 years, had been fixed because of the brutality of the killing and because he had hidden her body.
However, his lawyers argued that Leathem had actually left the body where it could easily be discovered, unlike in the case of Alexander Pacteau, who had murdered student Karen Buckley and attempted to dispose of her body in an acid bath.
Pacteau was also sentenced to a minimum of 27 years. The judges in Edinburgh agreed, and reduced Leatham's minimum term to 23 years.
A statement posted on the Justice For Paige Facebook page said: "The man who brutally murdered a 15-year-old defenceless child has been given more time off his sentence.
"He will only have to serve 23 years. There is no words to describe how we feel.
"It's heartbreaking and serves no justice to Paige and her family. She had her whole life ahead of her and it's been ripped apart. In 23 years her killer will walk the streets."
In delivering his ruling, appeal judge Lord Turnbull said of Leathem: "The appellant in the present case engaged in a brutal, savage and frenzied attack on a young defenceless child before attempting to cover up his actions.
"In the course of that attack, he appears to have struck her in the region of 146 times.
"Each case must be determined upon its own facts and those just identified demonstrate that the appellant committed a most appalling murder.
"Even in such cases though, all of the relevant circumstances require to be given proper weight before the appropriate sentence can be identified.
"The appellant was a family man of previous good character who had not offended before and who had expressed remorse. The murder was not premeditated."
He added: "When these circumstances are all taken account of, we think it can be said that the length of the punishment part selected in this case was inconsistent with current sentencing practice and was excessive."
A shop owner who murdered schoolgirl Paige Doherty in a frenzied knife attack has had his sentence reduced.