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The Giallorossi clinched top spot in Group A with a 3-1 win at the Stadio Olimpico - with Calafiori's first-time rocket early in the second half giving Paulo Fonseca's side the lead after they had gone behind early on.
It was Jean-Pierre Nsame who had given the Swiss side the lead, one they almost held onto until the break - until Borja Mayoral added to his tally in this competition with a poacher's header after Pedro's initial effort had been saved.
When Calafiori rifled in from 30 yards shortly after the restart the home side looked firmly in control, and victory was duly sealed with 10 minutes remaining as substitute Edin Dzeko steered home in style.
There was still time for some more late drama, however, as Young Boys defender Mohamed Camara was shown a straight red card after he inexplicably lashed out at Henrikh Mkhitaryan.
With qualification and top spot now secured, the Giallorossi have nothing to play for as they close out the group stage away to CSKA Sofia next week.
They are back in Serie A action at the weekend - Sassuolo the visitors to the Olimpico on Sunday.
ROMA 3-1 YOUNG BOYS
GOALSCORERS: Mayoral (44'), Calafiori (59'), Dzeko (81'); Nsame (34')
ROMA (3-4-2-1): Pau Lopez; Ibanez (Spinazzola), Cristante (Fazio), Juan Jesus; Bruno Peres, Villar (Pellegrini), Diawara, Calafiori; Carles Perez, Pedro (Mkhitaryan); Borja Mayoral (Dzeko)
Unused subs: Berti, Mirante, Karsdorp, Kumbulla, Bove, Ciervo, Milanese
YOUNG BOYS (4-3-3): Von Ballmoos; Hefti, Camara, Zesiger, Lefort; Rieder (Sierro), Aebischer (Gaudino), Garcia (Elia); Fassnacht, Nsame (Siebatcheu), Ngamaleu (Mambimbi)
Unused subs: Neuenschwander, Faivre, Sulejmani, Burgy, Maier, Maceiras
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