For the second week in succession, the English striker's solitary goal - his 20th of the season in all competitions - was enough for Jose Mourinho's side to grab the three points.
The No. 9 latched onto Nicolo Zaniolo's inviting pass to lash past Juan Musso just after the half-hour mark, in what ultimately proved to be the game's decisive moment.
The Giallorossi had further chances throughout the game, although as the second half wore on it was the visitors who pushed with more determination for an equaliser - but some resolute defending ensured it was never found.
In injury time both Marten De Roon and Henrikh Mkhitaryan received red cards, a dramatic end to a game played with intensity and determination throughout.
The result reawakens Roma's European qualification hopes, bringing them back in touch with their opponents and the rest in the race for the top six.
Jose Mourinho's side are back in action on Thursday, as they meet Vitesse Arnhem in the first leg of their Europa Conference League last-16 tie in the Netherlands.
Their next Serie A encounter is away to Udinese next Sunday.
ROMA 1-0 ATALANTA
SCORER: Abraham (32')
ROMA (3-4-1-2): Rui Patricio; Mancini, Smalling, Kumbulla; Karsdorp (Ibanez), Cristante, Mkhitaryan, Zalewski (Vina); Pellegrini (Sergio Oliveira); Zaniolo (Veretout), Abraham (Afena-Gyan)
ATALANTA (4-2-3-1): Musso; Hateboer, Demiral, Palomino (Djimsiti), Zappacosta (Pezzella); De Roon, Freuler; Miranchuk, Koopmeiners (Boga), Pessina (Malinovskyi); Pasalic (Muriel)
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