Bereft of the talismanic Ronaldo, who is self-isolating after testing positive for COVID-19 while on international duty with Portugal, Juve looked far from their best at Stadio Ezio Scida.
Alvaro Morata's first goal since rejoining the club on loan from Atletico Madrid cancelled out Simy's early penalty for the hosts, but their hopes of going on to claim all three points were dealt a blow with 30 minutes remaining when Chiesa, who joined on loan from Fiorentina on transfer deadline day, received a straight red card.
Crotone started with a spring in their step and were rewarded after 11 minutes when Simy stroked home from the penalty spot after Leonardo Bonucci had been adjudged to have fouled Arkadiusz Reca inside the area.
Juve bounced back nine minutes later when Morata slid home from four yards after being picked out by Chiesa.
Manolo Portanova - making his first appearance since May 2019 - was denied by Alex Cordaz at his near post shortly before the interval, while at the other end Buffon denied Pedro Pereira.
Rodrigo Bentancur flashed an effort wide immediately after the restart before Luca Cigarini whipped wide of Buffon's left-hand post from a promising position on the edge of the area.
Chiesa then saw red for a late challenge on Cigarini, although Andrea Pirlo's men almost stole ahead soon after when Morata flicked a header onto the post.
The Spain striker was denied a second inside the closing 15 minutes, with a VAR review showing that he was marginally offside when he turned home Juan Cuadrado's low ball into the area.
A point moves Juve up to fourth, four points behind leaders Milan, while Crotone are off the bottom after picking up their first point of the season.
Juve lack goal threat without Ronaldo
Pirlo might feel his side should be returning to Turin with all three points, given the late drama surrounding Morata's disallowed strike, but Crotone were good value for a point. They reduced their more illustrious opponents to just two shots on target - a statistic it is not hard to imagine would have been significantly higher had Ronaldo been available.
Morata does his bit up top
Morata did his best to cover for Ronaldo's absence, opening his account in his second spell at the club, hitting the post with a deft header and coming agonisingly close to grabbing a late winner. Pirlo will demand more from his hold-up play, however, given he lost possession a whopping 20 ti
