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Looking to leapfrog the visitors into the Champions League places in Serie A, the Giallorossi had to come from behind after Krysztof Piatek's poacher's goal midway through the first half.
Only a fine goalkeeping performance from Gianluigi Donnarumma denied Roma scoring on a number of occasions - with Nicolo Zaniolo's emphatic finish moments after the restart ultimately proving their only strike.
The draw means Eusebio Di Francesco's side remain fifth in the league table - a point and a place behind the Rossoneri.
On a night where the home fans made their feelings clear following the Coppa Italia exit in midweek, only Donnarumma's heroics denied Roma a much-needed three points.
The Italy international denied Edin Dzeko, Patrik Schick and Zaniolo at points during the game - while the woodwork came to his aid as Lorenzo Pellegrini's late header crashed away off the outside of the post.
Robin Olsen was far less busy at the end - he could do little for Piatek's close range opener, although he did make a start stop in the closing minutes to deny substitute Diego Laxalt.
Roma, emboldened as the game went on, pushed for a winner - but in the end had to settle for a share of the points.
They are now five games unbeaten in the league - and travel to Chievo on Friday.
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