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.
Palacio then looked to have sealed the points for Inter when he met a Jonathan delivery with a superb half-volley that sailed into the bottom right corner in first-half injury time.
But Livorno found a way back into the game when top scorer Paulinho struck his 12th league goal of the season, before substitute Innocent Emeghara ensured a share of the spoils five minutes from time.
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.
Di Natale - who has hinted that he may retire at the end of the campaign - finished off a sweeping team move to net his 11th Serie A goal of the season following good work from Allan and Bruno Fernandes.
The result makes it just one defeat in five for Udinese, while Catania remain six points off safety.
