The attacker's goal helped the Black and Greens to a 5-3 home win at MAPEI Stadium - Citta del Tricolore.
It was the 31-year-old's second goal in three Serie A matches for his new side, and his third strike in four games in all competitions, having netted against Ternana in the Coppa Italia.
Genoa, interestingly, drew first blood in Sunday's matchday three fixture through Krzysztof Piatek, before Boateng hit back for the home side in the 34th minute.
Pol Lirola then put Sassuolo in front for the first time with a strike four minutes later.
Khouma Babacar netted on 41 minutes to make it 3-1 before a Nicolas Spolli own goal sent Sassuolo into the break with a 4-1 lead.
Back from recess, Gianmarco Ferrari struck for the home side again, but Goran Pandev and Piatek scored two goals to reduce the deficit for the away team.
The result has left Sassuolo second on the table, while Genoa sit a lowly 15th.
Boateng joined the Black and Greens from German side Eintracht Frankfurt in July.