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Rudi Garcia's Roma side sought to move within one point of Serie A leaders Juventus at the Stadio Olimpico ahead of the mid-season break on Saturday.
And Roma produced the better of the first-half chances with the impressive Gervinho forcing Diego Lopez in a smart save after jinking his way into the penalty area.
The hosts thought they should have had a penalty before the break when Nigel de Jong handled in the area, but referee Nicola Rizzoli was uninterested.
Milan's hopes of earning a victory that would have moved them level with third-placed Napoli were dealt a blow in the 71st-minute when Pablo Armero received a second yellow card and subsequent red for deliberate handball.
The numerical advantage failed to yield a winner for Roma, though, despite another mazy run from Gervinho - who was again denied by Lopez from close range in injury time.
At the Stadio Citta del Tricolore, Sassuolo were looking to return to winning ways on home turf against Cesena having drawn at Roma and lost at Palermo in their last two Serie A outings.
It looked as though that would be the case when Italy striker Simone Zaza opened the scoring from the penalty spot in the 76th minute for his fifth league goal of the campaign.
However, there was a late twist for 19th-placed Cesena when Ze Eduardo rescued a point in the fourth minute of injury time.