Ivan Perisic gave the visitors the lead in the 53rd minute with his fourth goal in as many games after being put through by fellow Croatian Marcelo Brozovic.
Roma, who had an effort by Egyptian Mohamed Salah ruled out for offside in the 36th minute, equalised through Radja Nainggolan in the 84th when he turned in a poor shot on goal from Edin Dzeko.
The draw denied Inter the chance to close the gap in the fight for third position.
Third-placed Roma now have 60 points, four adrift of Napoli and seven behind leaders Juventus who face Torino in the Turin derby on Sunday. Inter are fourth on 55.
Palermo stayed just above the relegation zone thanks to a goalless draw at Empoli in Saturday's other match.
Napoli host 12th-placed Genoa on Sunday while Fiorentina, who are fifth, travel to Frosinone.
(Writing by Clare Fallon; Editing by Tony Jimenez)
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