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The seven-time European champions' only defeat of 2019 so far was a 1-0 Super Cup loss to Juventus in Saudi Arabia, and they are unbeaten in their last nine league matches.
Milan struggled for long periods to break down a stubborn Sassuolo outfit at the San Siro, with Spanish full-back Pol Lirola bundling the ball into his own net for the only goal 10 minutes before half-time.
Sassuolo saw goalkeeper Andrea Consigli sent off in the 64th minute for bringing down Krzysztof Piatek when the Polish striker was about to tap into an empty net, although Milan failed to find a second.
But it was enough to see them move one point clear of Inter, who were beaten 2-1 at Cagliari on Friday, with Roma just three points further back in fifth ahead of their capital-city derby against Lazio later on Saturday.
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Victory for Lazio would also move them within six points of fourth-placed Inter as the race for Champions League qualification intensifies.