The club, promoted from Serie B last season, was penalised for its links to the “Calcioscommesse” match-fixing scandal that has engulfed Italian football.
The Italian Football Federation said its decision was based on the downgrading of the charge against Pescara midfielder Gianluca Nicco from one of “sporting fraud” to one of “failing to disclose information” to authorities.
Nicco had been originally banned for three years but this has been reduced to a one-year suspension.
Atalanta are now the only Serie A side to start the 2012-13 season with a points penalty, with their two-point deduction upheld.
In the lower divisions, Albinoleffe’s punishment was reduced from 15 to nine points.
The Calcioscommesse scandal has seen individual players punished more heavily than the clubs for their actions.
Four players – Luigi Sartor, Mario Cassano, Alessandro Zamperini and Nicola Santoni – received five-year bans, while former Italy midfielder Stefano Mauri was briefly detained before being placed under house arrest.
Italy left-back Domenico Criscito missed out on Euro 2012 after he pulled out following questioning by police.