While the Serie A side were held to a 0-0 home draw against CSKA Sofia after their win at Young Boys, the Romanian champions took a point at home to the Swiss side following opening night success in Sofia.
For Cluj, Mario Rondon's second goal in as many games proved insufficient for all three points as the visitors from Berne equalised soon after to record a welcome 1-1 draw.
They then faltered badly at the weekend, losing 2-1 at home to unfancied Gaz Metan - a result which leaves them third in the table, six points adrift of top spot.
Nonetheless, the Transylvanian team's fans will have fond memories of their first meeting with Roma in 2008, as it was the club's very first Champions League fixture, in which they surprisingly defeated the Giallorossi 2-1 at Stadio Olimpico.
While Cluj have scored in all four previous matches played against Thursday's opposition, they have returned to Italy three times since that startling debut and lost each and every game - including 1-0 at the Olimpico against Roma's bitter rivals Lazio last season. Dan Petrescu's side have also lost six of their nine away fixtures in the Europa League post-qualification stages.
However, the domestically dominant Romanian club - who completed a hat-trick of league titles in the summer - are far from pushovers at this level.
Last term, the Railwaymen enjoyed a club record 16-match European journey that first built up steam in the Champions League first qualifying round and only hit the buffers in the Europa League last 32, where they narrowly went out to eventual winners Sevilla on the away goals rule.
Thursday night's hosts, though, have a particularly intimidating recent record.
Roma have only lost one of their previous 16 European fixtures in the Italian capital - winning 11 - and that was to Real Madrid. Not only that, but they remain unbeaten at home in the brief but growing history of the Europa League group stage.
Domestically, the Giallorossi are now five points behind league leaders AC Milan in eighth place after a comprehensive 2-0 win over Fiorentina at the weekend - the dominance of which was scarcely represented by the scoreline. That provides the perfect platform for Paulo Fonseca's men to take on a potentially tricky tie.
The Portuguese coach rewarded his players with a day off to recuperate ahead of Thursday's game and will expect a similarly convincing performance from his second-string side. Fringe players such as Borja Mayoral, Gonzalo Villar and Federico Fazio will again need to step seamlessly into the lineup as Roma continue to negotiate a hectic pre-Christmas schedule.
Roma Europa League form: WD
Roma form (all competitions): WWWDDW
CFR Cluj Europa League form: WD
CFR Cluj form (all competitions): DWWWDL
Coach Fonseca is also without the suspended Gianluca Mancini for this game, with Chris Smalling likely to be rested too, so Marash Kumbulla will step into defence alongside Brazilian centre-back Roger Ibanez.
Borja Mayoral is again set to lead the line, with Edin Dzeko available on the bench in event of emergencies.
Cluj coach Petrescu has a near fully-fit squad to choose from, having rotated heavily for their weekend reverse in the Romanian league.
Former Anderlecht forward Alexandru Chipciu can be utilised as a 'false nine', but Croatian striker Gabriel Debeljuh - who has had Italian experience with Piacenza in the past - is favoured to start up front in a 4-2-3-1.
A back-to-back goalscorer in Europe, well-travelled veteran Mario Rondon will start behind Debeljuh, while talented ex-Marseille man Billel Omrani can provide a second-half threat from the bench.
Roma possible starting lineup:
Lopez; Fazio, Ibanez, Jesus; Peres, Cristante, Villar, Spinazzola; Mkhitaryan, Pedro; Mayoral
CFR Cluj possible starting lineup:
Balgradean; Susic, Vinicius, Burca, Camora; Hoban, Djokovic; Rondon, Paun, Deac; Debeljuh
We say: Roma 2-1 CFR Cluj
Not a straightforward encounter for the Giallorossi, but a significant opportunity to strike out ahead of their opponents in Group A.
Cluj fans have fond memories of the Olimpico, but Thursday's clash is more likely to be reminiscent of their most recent forays to Italy - returning home pointless - as the Romanian champions lack the individual quality to cope with Roma's experienced continental campaigners.