The Giallorosse - who gave debuts to no fewer than five players - went toe-to-toe with the illustrious opponents, but when the second half deadlock was broken through Nora Heroum the game quickly got away from them.
Dominika Conc and Valentina Giacinti added late goals, adding an aspect to the final scoreline that perhaps did not reflect the action on the pitch.
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Both sides started the match with intent, although it was Milan that created the better of the first half chances. Goalkeeper Rosalia Pipitone was equal to everything however - while at the other end, Annamaria Serturini went close with an ambitious volley.
In the second half Betty Bavagnoli's side seemed to grow in confidence and conviction, with Manuela Giugliano hitting the crossbar with a fine free-kick.
But it felt like a game that would turn on the opening goal and so it proved, as Heroun's strike quickly turned the game fully in the visitors' favour.
Roma are back in action next week - as they travel to Fiorentina to face last season's Serie A runners-up in another huge contest.
See more photos from Sunday's game in our gallery.
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