The Colombian's dreadful back pass allowed Innocent Emeghara to equalize late on after the Nerazzurri had been 2-0 up at halftime
Hernanes and Rodrigo Palacio had put Walter Mazzarri's men 2-0 up at the break, and despite Paulinho's rocket to make it 2-1, it seemed the Nerazzurri would hold on.
However, Guarin's poor back pass allowed Innocent Emeghara to slot past Samir Handanovic with just five minutes remaining to extend Inter's winless run in Serie A to three.
Both sides struggled to create opportunities early on, although Inter goalkeeper Samir Handanovic was forced to tip Emerson's free kick over the crossbar after 15 minutes.
Brazilian playmaker Hernanes broke 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.
Livorno keeper Francesco Bardi could do nothing as Mazzarri's side extended the lead in first-half injury time. Palacio met 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 back pass from Guarin to slot past Handanovic, and make it an unhappy return to his former club for Mazzarri, whose current side remains fifth after the clash.