Miralem Pjanic put the hosts into the lead on 21 minutes before Pablo Osvaldo made it two 10 minutes later.
Mattia Destro added a third after 51 minutes to put Roma into a comfortable position, before a moment of madness from Osvaldo threatened to undo their good work
The Argentina-born Italy striker received a straight red card for elbowing Atalanta defender Carlos Matheu at a corner.
Atalanta came back into the match and Maarten Stekelenburg was forced into a brilliant save to deny Facundo Parra before the visitors had a penalty claim waved away.
But the Giallorossi weathered the storm to make light of the numerical disadvantage and record a fifth straight win.
They will now meet either Udinese or Fiorentina – who play next week – in the quarter-finals.