Inter surge seven clear in Serie A
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.
Brazil right back Maicon then charged forward in his inimitable style to bury a left-foot shot 10 minutes from time.
"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."
Samp, hammered 5-1 at Juve on Wednesday, had the ball in the net twice through Daniele Mannini and ex-Bari forward Antonio Cassano but both goals were rightly ruled out for offside.
Barreto then missed a late penalty for visitors Bari before they had an injury-time goal controversially chalked off for offside.
AS Roma, whose angry fans set off a letter bomb at their training ground on Friday, have been on a worse run than Samp but ended the slide with a 2-1 comeback win at home to Bologna.
Simone Perrotta grabbed the winner seven minutes into the second half after Jeremy Menez's shot was blocked.
City rivals Lazio and their coach Davide Ballardini remain in difficulty after a 1-1 draw at bottom side Siena, playing under new boss Marco Baroni for the first time.
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.
Lazio were again fortunate in another incident when the officials changed their minds having initially given Siena a spotkick and dismissed goalkeeper Fernando Muslera.
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.
Genoa drew 0-0 at Palermo in an entertaining late game to miss the chance to move level with fourth-placed AC Milan, who beat Parma 2-0 at the San Siro on Saturday.