Henrikh Mkhitaryan's late goal proved to be nothing more than a consolation for the Giallorossi at San Siro, as Jose Mourinho endured a disappointing return to his former stomping ground.
Denzel Dumfries, Marcelo Brozovic and Lautaro Martinez grabbed the goals for the Nerazzurri, who temporarily moved top of Serie A as a result.
The Giallorossi had chances - Gianluca Mancini heading inches wide just moments before Dumfries' opener - but a determined finish to the contest came too late to change its destiny.
Roma are back in action on Thursday; they travel to face Leicester City in the first leg of their Europa Conference League semi-final.
Their next Serie A meeting is against Bologna on Sunday night at the Stadio Olimpico.
INTER 3-1 ROMA
GOALSCORERS: Dumfries (30'), Brozovic (40'), Lautaro (52'); Mkhitaryan (85')
INTER (3-5-2): Handanovic; Skriniar, De Vrij, Dimarco (Bastoni); Dumfries, Barella, Brozovic (Gagliardini), Calhanoglu, Perisic (Gosens); Dzeko (Correa), Lautaro (Sanchez)
ROMA (3-4-2-1): Rui Patricio; Mancini, Smalling, Ibanez; Karsdorp, Mkhitaryan, Sergio Oliveira (Bove), Zalewski (Vina); Pellegrini (Veretout), El Shaarawy (Perez); Abraham (Shomurodov)
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