Jose Mourinho's side edged a narrow encounter with Sheriff Tiraspol on the opening matchday, while Servette lost on their group stage debut to Slavia Prague.
Match preview
While being the masters of the minor UEFA competitions in the past two seasons, Roma only narrowly got the better of Sheriff in Transnistria two weeks ago.
That hard-fought win was one of the few high points in what has been a dreadful start to the season for Mourinho and Roma.
Roma have taken on the moniker of 'flat-track bullies' given their only league wins have come against an Empoli side who were bottom, and newly-promoted Frosinone this season.
The thrashing of Empoli means only Inter Milan and Napoli have scored more goals than the Giallorossi, despite them being down in 13th.
A 4-1 defeat at Genoa last midweek has summed up their slow start, but they will hope that Europe can provide a welcome distraction for now from their domestic struggles.
Roma needed some Romelu Lukaku brilliance to get them over the line against Sheriff, scoring a fine individual goal which turned out to be the winner.
The Belgian's strike against the Moldovan champions also continued a remarkable run which has seen Lukaku now score in 12 straight Europa League games.
Since scoring in 2-0 win away at Wolfsburg for Everton back in 2014, Lukaku has netted 16 goals in those 12 matches, with that strike in Tiraspol being his first in Europe for Roma.
Tasked with keeping the big striker out will be Rene Weiler and his Servette side this midweek.
The European group stage debutants face a first ever competitive trip to Italy, but do so on the back of a poor start to the campaign.
Outside of two cup wins against lower-league opposition, Servette have won just two of their other 14 games so far.
Defeat at home to Slavia on matchday one continued that stuttering start, and their form on the road in Europe does not offer much hope either, considering they have just one win in their last six trips on the continent.
However, Weiler will hope that the fact Servette ended an eight-game winless run by defeating Lausanne at the weekend can be the catalyst to turn their fortunes around.
Roma Europa League form:
W
Roma form (all competitions):
L
W
W
D
L
W
Servette Europa League form:
L
Servette form (all competitions):
L
L
L
L
D
W
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Team News
Mourinho utilised his squad when rotating against Sheriff, and even though they needed bailing out by Lukaku, Roma could line up similarly.
Renato Sanches started in Moldova, but the new arrival has since picked up an injury which will keep him out of this one.
The hosts will be without a number of defensive options, with Chris Smalling, Diego Llorente and Marash Kumbulla all missing.
Those absentees could force Bryan Cristante into defence once more, after starting there against Frosinone at the weekend.
Smalling's English compatriot Tammy Abraham is also out after tearing his ACL in pre-season.
Servette have just two players out with injury in comparison, with Alexander Lyng and Theo Magnin both out.
The Swiss side's key man Miroslav Stevanovic enters the game in fine form having scored in his last two matches.
Swiss-born Cypriot international Joel Mall regained his place in the side for the win over Lausanne, after being only a substitute in the previous four games.
Roma possible starting lineup:
Svilar; Ndicka, Cristante, Mancini; Kristensen, Pellegrini, Aouar, Spinazzola; El Shaaraway, Lukaku, Zalewski
Servette possible starting lineup:
Mall; Tsunemoto, Rouiller, Onguene, Mazikou; Stevanovic, Cognat, Antunes, Douline; Guillemenot, Bedia
We say: Roma 3-1 Servette
Roma have underwhelmed massively so far, but like in the last two European campaigns, matches on the continent have provided much-needed respite.