The Lagunari also got off the mark last time out, leaving them just two points behind their capital-city counterparts in the standings.
Match preview
Having put just three points on the board from four matches, Roma's board saw fit to sack club legend Daniele De Rossi earlier this month and appoint ex-Torino coach Ivan Juric to replace him.
Despite being faced by fan protests last weekend, the Giallorossi then managed to post their first win of the season, beating in-form Udinese 3-0 via goals from Artem Dovbyk, Tommaso Baldanzi and Paulo Dybala.
Having made such a strong start in tough circumstances, Juric then attempted to lead his new side to victory on the Europa League's opening matchday, and they were on course for more success when Dovbyk struck during the first half against Athletic Bilbao.
However, an 85th-minute equaliser allowed the Basque side to leave Rome with a point, slightly taking the shine off another positive performance.
Stretching back to last season, Roma have now won only two of their last seven home matches in all competitions, after winning five of the previous six, and that represents a real problem for Juric and co to fix.
Nevertheless, the Giallorossi have still scored in 23 consecutive Serie A fixtures at Stadio Olimpico - their longest such streak since 2017 - and have also found the net in all of their last 19 league games against Sunday's visitors.
Such is the weight of history stacked against Venezia this weekend, they will be seeking their first top-flight away win over Roma since 1947: the Lagunari have failed to win any of eight subsequent contests in the capital.
Current coach Eusebio Di Francesco now returns to his former club hoping to end that long drought, having celebrated his 300th game and 100th victory as a Serie A manager by beating Genoa last week.
With just one point from four games, Venezia occupied last place in the table and had already crashed out of the Coppa Italia, failing to even score a single goal since the opening matchday.
However, last term's top scorer en route to promotion through the Serie B playoffs, Joel Pohjanpalo - who also missed a penalty - popped up with a late second goal to follow Gianluca Busio's opener at Stadio Penzo.
Over a third of Di Francesco's century of wins came while in charge of this week's hosts, but he has yet to engineer a single Serie A success against them: Roma are the opponent he has faced the most times without ever winning, losing nine of 12 previous meetings.
Roma Serie A form:
Roma form (all competitions):
D
L
D
D
W
D
Venezia Serie A form:
L
D
L
L
W
Venezia form (all competitions):
L
L
D
L
L
W
Team News
Following his strike against Udinese, Paulo Dybala is only one goal shy of joining Gonzalo Higuain (125) in third place on the list of highest-scoring Argentinians in Serie A history; however, he may be denied a chance to catch his compatriot this week.
The absence-prone forward was forced off at half time of Thursday's game against Athletic Club due to a muscular problem, so Matias Soule should step into Roma's attack, supporting in-form striker Artem Dovbyk.
Captain Lorenzo Pellegrini is expected to return from a knee issue that ruled him out in midweek, leaving Enzo Le Fee, Alexis Saelemaekers and possibly Dybala and Zeki Celik on the sidelines.
Meanwhile, Venezia can welcome Hans Nicolussi Caviglia back from suspension, but Bjarki Bjarkason is still injured and both Alfred Duncan and Giorgio Altare remain doubts.
After earning an overdue win last time out, Eusebio Di Francseco may be loath to make many changes, so Joel Pohjanpalo should again join Gaetano Oristanio up front, with USA international Gianluca Busio breaking forward from midfield.
Roma possible starting lineup:
Svilar; Mancini, Ndicka, Hermoso; Abdulhamid, Pisilli, Cristante, Angelino; Soule, Pellegrini; Dovbyk
Venezia possible starting lineup:
Joronen; Idzes, Svoboda, Sverko; Candela, Andersen, Nicolussi Caviglia, Busio, Zampano; Oristanio; Pohjanpalo
We say: Roma 2-0 Venezia
Fired up by their failure to finish the job last time out, Roma should make a fast start against Venezia, who have conceded the most goals during the first 30 minutes of play in Serie A this season - at an average of one per game.