Ex-AC Milan forward Stephan El Shaarawy put Roma ahead on his return to San Siro but Matias Vecino ensured a share of the spoils for Inter.
Matias Vecino snatched a point four minutes from time but Inter's winless run in Serie A continued as Roma left San Siro with a 1-1 draw.
Eusebio Di Francesco's side entered the match amid mounting speculation over Chelsea launching a bid for top scorer Edin Dzeko, but it was former AC Milan forward Stephan El Shaarawy who came to the fore with a coolly taken 31st-minute opener.
Mauro Icardi led Inter's charge during the closing stages as Brazil goalkeeper Alisson produced a pair of world-class saves to deny the Argentina striker.