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Stephan El Shaarawy gave the Giallorossi the lead with a brilliant curling strike midway through the first half - but Inter got back on terms shortly after the break, as Ivan Perisic headed home at the back post.
Both sides had chances throughout the contest to grab a decisive second goal, but in the end seemed relatively content to share the spoils - although Aleksandar Kolarov did force a fine save from Samir Handanovic in the closing moments.
With Lazio losing and Milan drawing elsewhere during the day, the point means Roma remain firmly in the hunt for the top four in Serie A, and a place in next season's Champions League.
The Giallorossi certainly started brightly in Milan, with Kolarov going close with a blistering drive inside the opening 10 minutes.
A miraculous save from Antonio Mirante from Lautaro Martinez then kept the scores level - before El Shaarawy produced his moment of magic, curling home from 20 yards out on his right foot, to unlock the match.
Inter struggled to respond but eventually got back on terms through Perisic. As the game wore on Lautaro, Icardi and Perisic all threatened - but it was perhaps Roma who had the better chances, as Lorenzo Pellegrini, Edin Dzeko and Kolarov threatened Handanovic.
Claudio Ranieri's side are back in action next Saturday, as Cagliari come to the Stadio Olimpico.
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