For the first time ever, the Catalonian side defeated the Old Lady in Turin thanks to an Ousmane Dembele goal in the first half and a late Lionel Messi penalty conversion, capping another excellent performance from the Argentine wizard a day after the resignation of club president and Messi adversary Josep Maria Bartomeu.
Barcelona's domestic season may be off to a rocky start, but they are perfect thus far in Europe, with two wins in two Champions League matches.
Barca coach Ronald Koeman later said: "We have been superior. We have had depth. It is a fair result.
"The only thing that has happened to us is that we have not converted more chances. Griezmann's has been bad luck, he has to keep working