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Substitute Jordan Veretout was at the heart of both second half goals as Paulo Fonseca's side made it 10 points from a possible 12 so far in Group A; as his inswinging free-kick was turned home by Cluj forward Gabriel Debeljuh moments after the break, before he converted a penalty 20 minutes later to wrap up the contest.
It seemed like the referee had misread the situation as Henrikh Mkhitaryan tumbled over the Cluj goalkeeper - but Veretout did not hesitate in taking advantage, adding yet another to his penalty collection.
After a somewhat underwhelming first half on a foggy, cold night, Roma sprung into life in the second period with the final scoreline perhaps not entirely reflective of some of the chances the Giallorossi created.
Borja Mayoral and Bruno Peres both had chances to join Veretout on the scoresheet, while at the other end Cluj never really looked like getting past Pau Lopez.
In the closing stages, with Fonseca managing his options, 18-year-old Filippo Tripi became the latest academy graduate to make his professional debut for the club.
Head-to-head record means Roma are now through from Group A with two games remaining.
They are back in Serie A action on Sunday - travelling to face Napoli in the Derby del Sole.
CLUJ 0-2 ROMA
GOALSCORERS: Debeljuh o.g. (49'), Veretout (67')
CLUJ (4-2-3-1): Balgradean; Susic, Manea, Burca, Camora; Djokovic, Itu; Rondon, Paun (Carnat), Pereira; Debeljuh (Vojtus)
Unused subs: Sandomierski, Checiches, Ciobotariu, Latovlevici, Haiduc, Chipciu, Joca
ROMA (3-4-2-1): Pau Lopez; Spinazzola (Mkhitaryan), Cristante, Jesus; Peres, Diawara (Milanese), Villar, Calafiori; Perez (Tripi), Pellegrini (Veretout); Borja Mayoral (Dzeko)
Unused subs: Berti, Mirante, Karsdorp, Pedro, Ciervo
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