A tight first half saw the deadlock broken just before the break by Leandro Greco, who guided home a free kick from 30 yards.
Sassuolo responded early in the second half to score their first ever goal in Serie A, with Simone Zaza the player to make history with a flick header.
The home side's parity was to last just three minutes, though, with Innocent Emeghara taking advantage of some poor goalkeeping to bag his fist for Livorno.
Paulinho doubled their advantage soon after, cutting inside to tuck away a low shot just inside the near post.
As Sassuolo chased a late response, Emeghara was able to exploit the space to get his second, dusting himself off to convert a penalty and make sure that Livorno earned maximum points.