Roma, who finished only four points behind Juventus last term, started the new campaign desperate to give Eusebio Di Francesco his maiden win.
Roma, who finished only four points behind Juventus last term, started the new campaign desperate to give Eusebio Di Francesco his maiden win as coach, having tasted title success with the Giallorossi as a player in 2001.
But in a tense encounter that saw new Atalanta signing Josip Ilicic hit the woodwork minutes from the final whistle, Di Francesco's men had to rely on Kolarov's 31st-minute free-kick to secure a season-opening victory.
After Andrea Masiello's naive foul on Belgium midfielder Radja Nainggolan, Serbian international Kolarov stepped up to roll a fine left-footed strike under the wall and beyond the reach of stunned goalkeeper Etrit Berisha.
Atalanta came fighting back in a tense finale with Ilicic, who signed from Fiorentina in the close season, coming closest to securing a share of the spoils when he hit the post from a yard out from Alejandro Gomez's searching pass.
Roma could have put the match beyond reach in injury-time when second-half substitute Stephan El Shaarawy rolled across for Edin Dzeko, but an alert Berisha was out quickly to smother.
Juventus, who claimed a record sixth consecutive title last season, opened their title defence with an easy 3-0 win at home to Cagliari on Saturday.
Napoli also got off to a winning start, by beating Verona 3-1.
Both AC Milan and Inter Milan, who face Crotone away and Fiorentina at home respectively, will aim to keep pace later Sunday.