The 33-year-old opened the scoring for Juve in the 50th minute, before adding a second just after 15 minutes.
He had a few golden opportunities to make it a hat-trick, but it was Sassuolo's Senegalese forward Khouma Babacar who found the back of the net one minute into second-half stoppage time.
It read: "I would like to apologize to all of Juventus fans for this misleading reaction in today's game. I'd like to emphasise that this isolated incident does not correspond with what I have always shown throughout my career". "As this was my first game I think it went pretty well I know that I can do better, but I'm happy to have helped the team", Can told Juventus' official website. It's also good timing, with the Champions League group stage beginning this week.
Unspectacular though it may have been, the five-time Ballon d'Or winner's first goal delivered a palpable sense of relief around the Allianz Stadium, where the hosts had struggled to create chances against their in-form visitors.
Giuesppe Pecoraro, who works as a prosecutor for the Italian Football Federation (FIGC) has confirmed Costa entire conduct will be monitored - so any ban would incorporate the elbow and head-butt.
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Here's to lots more Messi magic in the Champions League this season. Messi scored the opener with a brilliant free-kick.
Stephan El Shaarawy and Bryan Cristante put Roma, who lost to AC Milan before the global break, firmly in command at half-time.
The Argentine was the joint top Serie A scorer last season with 29 goals.
"This was a game we had under control, we should have killed it off".
AS Roma warmed up for their visit to Real Madrid on Wednesday by squandering a 2-0 lead and drawing 2-2 at home to lowly Chievo.
Juventus have lifted Serie A for the past seven seasons though haven't won the Champions League since 1996.