Miralem Pjanic and Pablo Osvaldo put Roma 2-0 up before the break after two howlers from Atalanta goalkeeper Andrea Consigli. Mattia Destro extended Roma's lead shortly after the interval.
Osvaldo swiftly went from hero to villain as he was shown a straight red card 10 minutes into the second period for an elbow on Atalanta defender Carlos Matheu.
Both sides had decent penalty appeals turned down.
Roma and Atalanta fielded almost full-strength line-ups, although Daniele De Rossi was handed a start for the first time in a month for the capital side.