Luca Cigarini came close in the fourth minute with a free kick that he curled narrowly over the crossbar.
Cigarini had another good chance when he worked some room on the edge of the box and fired in a powerful strike that forced a save from the keeper.
Atalanta dominated the first half and they deservedly took the three minutes before the break, when Denis directed a spectacular overhead kick into the top corner.
Sassuolo's hopes of equalising for the second time then suffered a blow when Simone Missiroli was sent off for picking up his second booking of the match.
With nine minutes left to play Atalanta were also reduced to 10 men as Giuseppe Biava earned a second yellow card, but his side managed to hold on and claim the win that has moved them seven points clear of the relegation zone.