Sassuolo looked for a quick response and Antonio Floro Flores tried his luck with a low free kick that was comfortably saved by the keeper.
However, the hosts did not have to wait too much longer to find the net, as Francesco Magnanelli fired a long-range effort into the top corner that left the keeper helpless.
The game continued at a frenetic pace and 11 minutes later Pinilla restored Atalanta's lead with a low strike into the bottom corner, despite the keeper getting a strong hand on the ball.
Once again the visitors were unable to hold onto their lead, as Floro Flores rifled a powerful strike into the top corner to ensure that the teams headed into the break on level terms.
Atalanta were dealt a further blow in the opening minutes of the second half, as Pinilla was sent off for a second bookable offence following a late challenge on Federico Peluso.
Despite their numerical advantage, Sassuolo struggled to create clear-cut chances and they too found themselves down to 10 men when Sime Vrsaljko brought down Moralez inside the box and was shown his second yellow card of the afternoon.
A penalty was given by the referee for the challenge, but Moralez saw his spot kick saved by Andrea Consigli as the match finished in a draw.