Juventus took the lead in the third minute when Paulo Dybala bounced home a volley.
Sassuolo hit back in the 23rd minute with Hamed Traore bending a superb effort past keeper Mattia Perin.
Both sides had chances in the second half but Juventus grabbed the winner in the 88th minute when Dusan Vlahovic wriggled through on the left and his shot deflected in off the arm of Ruan Tressoldi.
Fiorentina left it even later with Nikola Milenkovic scoring in the third minute of stoppage time at Atalanta.
Boga, who signed for Atalanta on loan from Sassuolo in January, put Atalanta ahead with a superb goal in the 56th minute.
Piatek's penalty was saved by Juan Musso but he converted the rebound to set up a tense finale.
Zappacosta struck a fierce shot against the bar before Fiorentina were reduced to 10 men in the 79th minute as Lucas Martinez Quarta earned a second yellow card for a foul on Luis Muriel. But there was a sting in the tail as deep into stoppage time Milenkovic's controlled a knock down and dispatched a stunning half-volley into the bottom corner.
A VAR check for a possible handball added to the tension, but the goal stood and Fiorentina could celebrate.