With morale high after a run of seven points from nine, Vincenzo Italiano's visitors may fancy their chances of another cup upset at Stadio Olimpico.
Once again, Roma came unstuck against one of Calcio's big boys on Saturday, as they were taught a lesson by ruthless Lazio in the Derby della Capitale - losing 3-0 to their bitterest rivals.
Having also been picked off on the counter attack in heavy defeats to Atalanta and Napoli, plus proving unable to turn draws against Juventus and Inter into wins, Paulo Fonseca's side are gaining a reputation as mere 'flat-track bullies' in the league.
Even so, a most likely much-changed XI will surely not have things all their own way against enterprising Spezia this week, as the nine-times Coppa winners take on the modest Ligurian team which has never lifted the trophy.
The clubs now come together twice in four days: first to decide who will meet Napoli in the cup quarter-finals, then in the 19th round of Serie A - with both games in Rome.
In fact, the fixtures played this week will double the number of previous encounters between two vastly different outfits, as Roma have only met Spezia once before - also in the Coppa Italia.
Against the odds, the lower-league Aquilotti emerged victorious at the Olimpico at this stage in 2015-16, after a goalless draw was followed by victory in a dramatic penalty shootout.
A second such surprise could happen again on this occasion, as a Spezia side which performed heroics to earn a point away to Torino at the weekend will travel south in superior form to their more illustrious Roman counterparts.
Two successive Serie A wins - against Napoli and Sampdoria - looked like they would be followed by defeat in Turin, when Italiano's side went down to 10 men in the eighth minute. However, they even managed to forge the best chances for the remainder of the match - with talented Azzurini midfielder Tommaso Pobega, on loan from Milan, impressing throughout.
That sort of spirit and unity - particularly considering star striker M'Bala Nzola was also missing through injury - helped Spezia keep their first clean sheet in nine games and could conceivably keep their cup run alive this week.
Wins over Citadella and then Bologna (after extra time) in the previous rounds have brought the Bianconeri into the limelight of a glamorous fifth round clash - with the final eight now within touching distance.
Roma form (all competitions): LWWWDL
Spezia Coppa Italia form: WW
Spezia form (all competitions): LLLWWD
Both sides will see a significant turnover in playing personnel amid a hectic league schedule and Paulo Fonseca may welcome the opportunity to 'rest' some of his troops after the dismal derby defeat on Saturday.
Gianluca Mancini will most likely continue in defence, as he is suspended in the league, with Marash Kumbulla and Federico Fazio joining him in the back three. Meanwhile, Bryan Cristante and Amadou Diawara could come into the midfield.
Spezia's Serie A talisman M'Bala Nzola is unlikely to return until the repeat fixture next weekend, so young Roberto Piccoli or Andrey Galabinov should start up front in Vincenzo Italiano's customary 4-3-3.
Roma possible starting lineup:
Lopez; Mancini, Fazio, Kumbulla; Peres, Diawara, Cristante, Spinazzola; Pedro, Perez; Mayoral
Spezia possible starting lineup:
Rafael; Vignali, Chabot, Dell'Orco, Marchizza; Deiola, Pobega, Saponara; Agudelo, Galabinov, Farias
We say: Roma 3-2 Spezia
Feeling the benefit of squad rotation after a disastrous weekend defeat, a new-look Roma should deal with the Aquilotti ('Little Eagles') far better than they did the Aquile.
Nonetheless, Spezia will not go out with a whimper, as they have consistently proved their commitment to attack - even on the grandest stages such as Stadio Olimpico.