Even without the suspended Maxi Moralez, Stefano Colantuono's men had enough firepower to see off the Tuscans with Giuseppe De Luca and German Denis netting the goals.
The win takes the Bergamo side to within four points of the top five, although Inter Milan, the side they beat at the weekend, are in action against Udinese on Thursday night and could pull seven points clear.
Livorno did not start off badly and Paulinho almost gave them an early lead, forcing Andrea Consigli to stretch to tip his shot over.
Atalanta then took charge of matters and wasted several chances before De Luca put them in front.
Denis saw one effort deflected behind before Francesco Bardi made a reflex save to deny him just minutes before the deadlock was broken.
De Luca's first headed effort came back to him off Denis, but he accepted the second invitation to score having seen a volley deflected wide moments earlier.
Livorno made a confident start to the second half, but like in the opening 45 minutes, they only had one effort to show for it with Innocent Emeghara's header saved by Consigli before they lost their way once again.
With their first attack of the second 45 minutes, Atalanta took the lead.
This time it was De Luca's turn to set-up Denis, who thanked him by placing his shot in from the edge of the penalty area.
Apart from long-range shots from Paulinho and Emeghara, Livorno did not go close to finding a route back into the game as their road to survival became more complicated in Bergamo.