Sassuolo had done more than enough to claim a share of the points when Kean struck two minutes from full-time.
A long ball out of defence from Leonardo Bonucci ended with Kean, a 67th minute substitute for Alvaro Morata, turning Vlad Chiriches and firing the ball between goalkeeper Andrea Consigli’s legs at the near post.
The last-gasp win keeps Juve in fouth place, eight points adrift of leaders AC Milan but, perhaps more significantly, eight points clear of Roma, who are chasing them for the final Champions League spot.
It was a frustrating loss for Sassuolo who were the better team for most of the game, posing problems from the outset when Davide Frattesi’s header at the near post from a Domenico Berardi corner kissed the crossbar on its way over.
Gianluca Scamacca was also sharp, forcing Juventus keeper Wojciech Szczesny into a fine save.
Juve’s first real attack almost brought reward when Paulo Dybala thought he had found the net, only for Frattesi to block at the last moment.
Sassuolo broke the deadlock for a deserved lead in the 39th minute.
Morata lost possession in midfield and Berardi produced a delightful backheel to send Giacomo Raspadori clear.
Raspadori’s powerful shot gave Szczesny no chance, but Juve were level on the stroke of half-time.
Dybala made light of an awkward angle to thrash the ball into the roof of the net despite Sassuolo’s claims that Morata fouled Giorgos Kyriakopoulos in the build-up.
That set the stage for Kean’s last-gasp heroics as Juve consolidated their place in the top four.