The home side drew level in the 71st minute through Filip Djuricic after good work from substitute Mert Muldur but Torino responded superbly with two swift goals.
But Sassuolo, who would have gone above AC Milan into first place with a win, replied with two quick goals of their own to ensure a share of the points.
A superb long distance strike from Chiriches reduced the deficit in the 84th minute before a header from Francesco Caputo made it 3-3.
The draw left Sassuolo on 11 points from five games, a point behind Milan who have a game in hand. Torino are second from bottom after picking up their first point of the season.