Livorno, who had won two out of two under new coach Serse Cosmi, had the better of the first half with Antonio Candreva's free kick forcing Julio Cesar into a stunning one-handed save.
Inter coach Jose Mourinho started Samuel Eto'o on the bench with one eye on Wednesday's Champions League clash at Dynamo Kiev but had to bring the striker on at halftime.
The effect was immediate with Livorno's defence dropping back and allowing Argentina's Milito to fire into the corner.
"Today we took a bit of a risk by rotating the squad," Mourinho told Sky television.
"They were better organised in the first half but we came out for the second with a new system and played with freedom."
Barreto then missed a late penalty for visitors Bari before they had an injury-time goal controversially chalked off for offside.
LETTER BOMB
Simone Perrotta grabbed the winner seven minutes into the second half after Jeremy Menez's shot was blocked.
Stefano Mauri gave the visitors the lead with a header but Massimo Maccarone equalised before team mate Abdelkader Ghezzal had his shirt ripped off his back by Lazio's Sebastiano Siviglia, only for the referee to wave away the penalty appeal.
Catania coach Gianluca Atzori's job also hangs in the balance after a 3-1 defeat at Fiorentina while Chievo drew 1-1 with Udinese and Cagliari overcame Atalanta 3-0.
