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Simone Zaza fired a strike just wide of the post in the opening stages as the visitors made a strong start to the match.
Berardi stepped up to take the resulting spot kick and although the keeper got a hand to the ball, his effort was powerful enough to find the net.
It took the hosts just six minutes to get back on level terms as Iago Falque was played through by Lestienne and he kept his composure to slot a low effort past the keeper.
The teams went into the break on level terms, but five minutes into the second half Sassuolo retook the lead as Simone Missiroli slotted in from close range after the hosts had failed to clear a corner.
Once again Genoa hit back almost immediately and within three minutes Ioannis Fetfatzidis rounded the keeper before slotting in for his side's second goal of the afternoon.
Despite coming under a huge amount of pressure from the hosts, Sassuolo took the lead for the third time as Zaza got to the byline and pulled the ball back for Berardi to finish.
It looked as if Sassuolo would hold out and win the match, but deep into stoppage time Francesco Magnanelli conceded a penalty and Fetfatzidis stepped up to convert from the spot to ensure a point for Genoa.