Gennaro Gattuso's side was second best during a poor first half but came out for the second period rejuvenated and secured all three points thanks to its young stars.

Milan's more adventurous approach bore fruit after 48 minutes when Cutrone got a delicate touch to Suso's cross, which flashed past Alisson.

Milan had further chances to add a second before the unlikely figure of Calabria added gloss to the scoreline with a composed finish in the 74th minute.

The win sets Milan up perfectly for a big week, which sees it face Lazio in a Coppa Italia semi-final second leg before a crunch derby with Inter four days later.

Roma, meanwhile, will need to pick itself up quickly after a second consecutive defeat ahead of a daunting trip to Napoli next weekend.

Roma started with a spring in its step and tested Gianluigi Donnarumma - celebrating his 19th birthday - twice inside the opening 10 minutes through Cengiz Under and Diego Perotti.

Milan soon settled, however, and largely kept its host at arm's length for large swathes of the first half.

When Roma did threaten, Lorenzo Pellegrini was at the heart of it. The 21-year-old midfielder had a penalty appeal waved away before flashing a shot wide of Donnarumma’s right-hand post as the half ended goalless.

In stark contrast to their tepid first-half display, Milan started the second period with verve and swagger and was rewarded with the opening goal after just three minutes.

Cutrone found Suso on the right and then stormed into the box to meet the Spaniard's teasing cross with an impudent flick past Alisson for his sixth Serie A goal of the season.

Perotti then drilled a long-range effort just wide as Roma attempted to restore parity, while Alisson had to be alert to parry over Franck Kessie's powerful drive as Milan looked to double its advantage.

The shackles were well and truly off Milan’s players after Cutrone's goal and Hakan Calhanoglu should have at least tested Alisson with a low drive just before the hour, instead dragging it wide.

Substitute Nikola Kalinic should have wrapped it up with 20 minutes remaining but was denied by a smart one-handed save from Alisson.

The Croatian made up it for it soon after, though, playing in the marauding Calabria who coolly clipped over the onrushing Roma goalkeeper for his first ever Serie A goal.

Roma rarely looked like clawing their way back into the game in the closing stages as Milan - which could have had a third late on through Fabio Borini - comfortably held firm to register a memorable win.