The battling victory put champions Inter level on points with AC Milan, who beat Chievo on Saturday, but Lazio's 2-0 win at Bari kept the Romans top of the standings by two points.
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Tricky playmaker Hernanes, one of the buys of the season from Sao Paulo, latched on to Italy midfielder Stefano Mauri's pass to give Lazio an early second-half lead before Sergio Floccari sealed the points from Mauri's mishit shot.
Juventus made a bad start but now lie just five points from the summit after a rampant 4-0 home win over Lecce sparked by Alberto Aquilani's first goal for the club.
Milos Krasic, distraught when Serbia's Euro qualifier in Italy was abandoned on Tuesday because of rioting away fans, was again superb before Alessandro Del Piero scored a late fourth to equal Giampiero Boniperti's Juve record of 178 Serie A goals.
In the early game, Cameroon's Eto'o took his league tally to six goals from seven games this season and, like most of his recent efforts, the 39th-minute goal was a marvellous strike.
Wesley Sneijder hooked on and Eto'o twisted and turned like Inter's serpent symbol on their new away kit before planting a left-foot shot into the corner from the edge of the box.
"Cagliari put us under pressure but we deserved the lead. Eto'o is enjoying a great moment and we hope he continues like this," Inter's Javier Zanetti, back from injury for Wednesday's Champions League clash with Tottenham Hotspur, told Sky.
Eto'o's strike was the perfect riposte to the Cagliari fans whose racist chants towards him caused the referee to suspend the game after three minutes.
The Italian football federation, which has long struggled with racist fans, gave referees the right to suspend matches in case of such chanting after Mario Balotelli was constantly abused in Inter's match at Juve
