The Giallorossi had their chances to win the game late on - with Gianluca Mancini hitting the post from close-range - but ultimately were forced to settle for a draw, as they failed to get revenge for the defeat they suffered in the first meeting.
Ola Solbakken and Erik Botheim both got on the scoresheet for the Norwegian visitors, but Jose Mourinho's side twice managed to respond.
First Stephan El Shaarawy curled in a trademark right-footed strike to revive his team, before Roger Ibanez grabbed a second equaliser with a header that goalline technology confirmed had crossed the line before being parried away by the Bodo goalkeeper.
That finish set up a frantic finale as Roma bombed forward in search of a winner - but none would be forthcoming, as they stay second in the group as a result.
Mourinho's side have one more game before the international break; they travel to face Venezia on Sunday night.
ROMA 2-2 BODO/GLIMT
SCORERS: El Shaarawy (54'), Ibanez (84'); Solbakken (45'), Botheim (65')
ROMA (4-2-3-1): Rui Patricio; Karsdorp, Mancini, Cristante, Ibanez; Darboe (Villar), Veretout; Zaniolo (Shomurodov), Mkhitaryan (Perez), El Shaarawy (Zalewski); Abraham (Mayoral)
BODO GLIMT (4-3-3): Haikin; Sampsted, Moe, Lode, Bjorkan; Fet, Hagen, Konradsen (Vetlesen); Solbakken, Botheim, Pellegrino (Mugisha)
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