The Italian started in his first appearance for the club but it was Alvaro Morata who left his mark after firing home, on an assist from the Fiorentina man, from close range in the first half to cancel out Simy’s spot kick.
A cagey second half was marked by Chiesa’s red as he was sent off for a stomp on Luca Cigarini, while Morata saw a second ruled out for a marginal offside call.
The first chance of the match fell to Simy, who sent an effort from a good position wide of the mark.
Crotone’s positive start was rewarded early on as Leonardo Bonucci’s mistimed tackle on Arkadiusz Reca resulted in a penalty for the home side. Simy made no mistake in sending Gianluigi Buffon the wrong way on the Italian’s 650th appearance.
The advantage lasted for just nine minutes though as Dejan Kulusevski picked out Chiesa with a through ball, and the Italian rolled the ball across goal for Morata to tap in from close range.
Juventus took the initiative from there, but there only real effort on goal came in the 42nd minute when surprise starter Manolo Portanova fired straight at Alex Cordaz.
There was time for Pedro Pereira to test Buffon at the back post just before the end of the half, but the Italian made sure to keep the effort out.
Rodrigo Bentancur hit a great volley from outside the box just after the restart but it whistled just wide of the mark, while Luca Cigarini responded at the other end but fired wide after finding space in the middle of the Juve defence.
Chiesa’s debut turned into a nightmare in the 60th minute when he was sent off for a studs-up challenge on Cigarini, though replays showed it may have been a tad harsh.
Morata sent a glancing header off the post before Cordaz claimed the ball off the line, and he was also denied in the 76th minute. Juan Cuadrado ran into the box and fired a wayward shot that was redirected home by the Spaniard for his second on the night, however replays showed he was marginally offside.
It proved to be the last major moment of the contest, with those in attendance cheering at the final whistle after seeing Crotone earn a well-earned point against the reigning champions.