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.
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.
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.
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.
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.
