The result was a big blow to Salernitana coach Filippo Inzaghi.
The former Juventus and AC Milan striker has yet to win any of his four league games since taking charge in October and the club remains rooted to the bottom of the Serie A table with just five points from 12 games.
Salernitana are the 30th team in the history of the Serie A not to win any of their opening 12 games of the league season. Of the previous 29, only three avoided relegation.
Boulaye Dia doubled their lead 12 minutes later when he hammered a shot into the roof of the net from 12 yards out. It was the Senegal striker's fourth goal of the season.
However, Norwegian midfielder Kristian Thorstvedt pulled the home side back by scoring a brace.
He netted his first nine minutes before halftime with a simple tap-in after Grégoire Defrel set him up with a looping header across goal, and equalised seven minutes into the second half with a right-footed strike.
The point lifted Sassuolo up one place to 14th.
The 21-year-old centre back volleyed home after some indecisive defending to provisionally lift the hosts to 13th spot.
Verona started the day third from bottom and Friday's defeat means they still haven't won a game since the end of August.