Former Inter hero Zlatan Ibrahimovic also grabbed his first league goal for AC Milan before Sergio Floccari equalised to seal a 1-1 draw for hosts Lazio in the fourth round of matches.
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Milan have only won once in the league this campaign but last season's runners-up AS Roma have yet to gain three points at all after a 2-1 defeat at promoted high-fliers Brescia where goalkeeper Julio Sergio was forced to play on despite injury.
Inter have also been less than fluent in their early games with Argentina's Milito, the goalscoring architect of their treble triumph last term, especially struggling for form.
However, the forward rediscovered his touch after 27 minutes when he nodded in Samuel Eto'o's cross at a relieved San Siro.
Strike partner Eto'o, who in contrast to Milito has sparkled this term after a quiet first season at Inter, then fired in two penalties after the break following Marco Rossi's handball and a foul on Lucio by Emanuel Rivas.
Milito had the final say when he finished off a late counter attack to crush Bari, who had struck the woodwork through Sergio Almiron in the first minute.
Inter, who lost defender Walter Samuel to injury, lead the standings on 10 points and next travel to Roma on Saturday after the Serie A players' strike was suspended.
It could be the perfect time for Inter to meet their main rivals for the title in recent years after winless Roma slipped to their second defeat of the fledgling campaign.
A Perparim Hetemaj strike and Andrea Caracciolo's 65th-minute penalty after Philippe Mexes was dismissed for a foul put third-placed Brescia ahead before Marco Borriello pulled one back and Adriano went close to an equaliser.
Roma keeper Julio Sergio then seriously injured his leg in stoppage when making a challenge he was booked for but with all substitutes used he was forced to play on in tears of agony.
Milan have almost made as bad a start as Roma under new coach Massimiliano Allegri and they lacked width at Lazio with Kevin Prince Boateng forced to play as part of a front three with Alexandre Pato injured and Robinho not fully fit.
Ibrahimovic broke the deadlock in the second half with a classy finish from Clarence Seedorf's pass but Floccari cleverly netted at the near post after a cross from the superb Hernanes.
Chievo moved back up to second with a 3-1 win at enigmatic Napoli, promoted Cesena's strong start ended with a 2-0 defeat at Catania and Udinese are still without a point after a 2-1 loss at Bologna.
