Bolivia beat Peru 2-0 at home then held Chile 0-0 away in the first week of September but FIFA's disciplinary committee awarded 3-0 walkovers to their opponents' in each case.
FIFA ruled that Bolivia had fielded Paraguayan-born Nelson Cabrera when he was ineligible to play. Bolivia have already lost an appeal to FIFA itself.
"In appealing to CAS, the Bolivia Football Federation (FBF) seeks to have the decisions...overturned in order to recover the FIFA 2018 World Cup qualification points it has lost," said CAS.
The forfeits have significantly affected the South American World Cup qualifying group, where the top four of 10 teams qualify directly for Russia and the fifth goes into an intercontinental playoff.
The two points Chile gained lifted them above Argentina by one point into fourth place, one of the automatic qualifying berths, and took them two clear of rivals Colombia.
Brazil (27 points), Uruguay (23) and Ecuador and Chile (both 20), are in the top four places, with Argentina fifth on 19 and Colombia on 18.
Peru are eighth with 14 points and Bolivia, who last qualified for the World Cup in 1994, one from bottom of the table with seven after 12 of the 18 matches.
(Reporting by Brian Homewood; Editing by Angus MacSwan)
