Walter Mazzarri's side appeared to be on their way to a comfortable victory after two first-half goals put them very much in command at the Stadio Armando Picchi.
Hernanes opened the scoring with his first goal for the club since joining from Lazio in January, slamming home from close range after Mauro Icardi had failed to connect with Rodrigo Palacio's knock back across goal.
The Switzerland international raced on to an ill-advised backpass from Fredy Guarin to coolly slot home and move Livorno one point adrift of safety and extend Inter's winless run to three games.
Elsewhere on Monday, bottom club Catania's slim prospects of survival were further dented by a 1-0 loss at Udinese.
Veteran striker Antonio Di Natale again proved to be Udinese's inspiration, scoring the only goal of the game in the 68th minute.
