Striker Emanuele Calaio's two-year ban, which was imposed as part of the same investigation, has also been reduced to four months.
Parma will have to pay a €20,000 fine while Calaio was fined €30,000 but will be eligible to play again on January 1st next year.
A 2-0 win at Spezia on May 18th saw two-time UEFA Cup winners Parma promoted to the top division just three years after a financial meltdown led to relegation from Serie A and rebirth in the semi-professional Serie D, Italian football's fourth tier.
Calaio, 36, was initially banned for two years for match-fixing after he sent text messages to a former team-mate that appeared to ask Spezia players not to try too hard.
Spezia fans reacted furiously to their team's display after the match, directing particular anger toward former Italian international and ex-Parma player Alberto Gilardino, who smashed a penalty for Spezia high and wide with the hosts still only a goal down.