Inter appeared to be in complete command after taking a commanding 2-0 lead at the Stadio Armando Picchi on Monday, but Livorno stormed back with Emeghara the hero as he found the net five minutes from time.
Hernanes gave Walter Mazzarri's visitors the lead with his first goal for the club since joining from Serie A rivals Lazio in January.
Argentine striker Rodrigo Palacio then seemingly put the game beyond doubt shortly before the interval, only for Paulinho to start the fightback for Livorno.
Livorno's top scorer struck with his 12th league goal of the campaign early in the second half, and there was to be a final twist in the tale as Emeghara capitalised on an error from Inter midfielder Fredy Guarin to earn a draw that moves them to within a point of safety.
Inter, meanwhile, remain fifth.
Both sides struggled to create opportunities early on, although Inter goalkeeper Samir Handanovic was forced to tip Emerson's cross-cum shot free-kick over the crossbar after 15 minutes.
Inter were frustrated for much of the first half despite controlling possession, but Hernanes went close to opening the scoring for the visitors when he curled narrowly wide from the edge of the area.
And the Brazilian playmaker did then break the deadlock in the 37th minute, slamming home from close range after Mauro Icardi had failed to make contact with a header back across goal from Palacio.
That goal appeared to boost Inter's confidence and only the fingertips of Livorno keeper Francesco Bardi prevented them from doubling their advantage as he turned a fierce long-range strike from Zdravko Kuzmanovic over the bar.
However, Bardi could do nothing as Mazzarri's side did extend their lead in first-half injury time, Palacio meeting Jonathan's right-wing cross with a clever half-volley into the bottom corner.
Inter carried that momentum into the second period and almost immediately added a third following the restart as Palacio forced Bardi into another fine save.
But the hosts got back into the game after 53 minutes when Paulinho rattled an effort in off the crossbar from Leandro Greco's well executed corner.
Former Siena striker Emeghara was thrown on in place of Ishak Belfodil - on loan from Inter - shortly after as Livorno pressed for a share of the spoils.
And the Switzerland international made no mistake late on as he raced on to a poor backpass from Guarin to slot past Handanovic and make it an unhappy return to his former club for Mazzarri.
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