Midfielder Hernanes, with his first goal since his January move from Lazio, and Rodrigo Palacio put Inter 2-0 ahead at halftime before Paulinho pulled one back and substitute Innocent Emeghara pounced on Guarin's terrible back pass to equalise.
Inter badly needed a win after their previous two games ended in a 2-1 defeat by Atalanta and goalless draw with Udinese, both at San Siro.
Monday's point, their 13th league draw of the season, left them clinging to fifth place which would earn them a Europa League place next season.
Hernanes put Inter ahead in the 37th minute when he fired home from inside the penalty area after team mate Mauro Icardi missed his kick.
Palacio then scored with a volley with the final kick of the first half, the Argentine's 14th league goal of the season, to put Inter seemingly in control.
Paulinho brought Livorno back into the game when he scored following a well-worked corner routine nine minutes after the break.
Inter coach Walter Mazzarri has blamed poor finishing for his team's troubles but it was a defensive mistake which cost them two points.
Guarin underhit an awful back pass from the halfway line which was intercepted by Emeghara and the Swiss calmly placed his shot past Samir Handanovic with five minutes left.
Livorno, 18th in the 20-team table, remained in the relegation zone with 25 points, although they are within one of Bologna.
In Monday's other game, 36-year-old forward Antonio Di Natale scored the only goal to give Udinese a 1-0 win over bottom club Catania.
Seventeen-year-old goalkeeper Simone Scuffet produced another impressive display for Udinese as he made two important late saves to guarantee the points.
- Sports & Recreation
- Rodrigo Palacio
- Innocent Emeghara