Baggio began his football career at age five in Tombolo, a province of Padova. He was spotted by Torino scouts at the age of 13 and taken into the Torino youth system. He made his debut in Serie A as a 19-year-old against Lazio and became a regular member of the starting line-up, making a name for himself as a promising youngster. He emerged as a tenacious, hardworking, consistent, and versatile defensive midfielder during his time at the club, who was capable of playing in several positions. With Torino, he won the 1989–90 Serie B title, followed by the 1991 Mitropa Cup. He was loaned to Inter at the age of 20 in 1991 for the 1991–92 season, making 27 appearances and scoring 1 goal.