Ali will have had revenge on his mind against the experienced Italian after their last-16 clash at the European Games earlier this year was stopped when Ali suffered a cut in the first round.
The teenager came out firing in the first round, with his jab making it difficult for the former Olympic bronze medallist to make his mark.
Two judges gave the first round to Picardi, who finished on the front foot, but there was also a 10-9 for Ali.
Both fighters connected with good shots in the second and it was Ali that shaded the scorecards to leave the bout wide open entering the third and final round.
Chants of 'Ali, Ali, Ali' came from the crowd during what was energetic third round, and it was Ali that came through 2-1 on points to book his spot in the next round.
Ali, on his debut at the World Championships, will fight Azerbaijan's second-seed Elvin Mamishzada in the quarter-finals on Saturday.