Mauro Icardi scored twice in the second half as Roma was made to pay for its profligacy, having hit the woodwork three times.
Spalletti left Roma by mutual consent at the end of last season and joined Inter shortly afterward, along with sporting director Walter Sabatini. He has two league wins out of two for Inter, after they beat Fiorentina 3-0 in their opener. Icardi also scored two then.
It appeared as if their return would be a miserable one after Edin Dzeko, last season’s top goal-scorer, gave Roma the lead. He chested down Radja Nainggolan’s pass and volleyed it home.
Aleksandar Kolarov hit the post seconds earlier and Roma hit the woodwork twice more through Nainggolan and Diego Perotti.
Inter leveled through Icardi from an Antonio Candreva assist in the 67th.
Icardi doubled his tally 10 minutes later, controlling Ivan Perisic’s low cross before swiveling to fire into the bottom left corner.
Matías Vecino sealed the result three minutes from time with his first goal since joining Inter from Fiorentina in the offseason.
There was controversy however, as Roma felt it should have had a penalty early in the second half when Milan Skriniar appeared to trip Diego Perotti at the byline, but the video assistant referee was not called upon and only a corner was given.