Playing in Trieste due to stadium troubles in Sardinia, Cagliari was put in front by Swedish midfielder Albin Ekdal in the 26th minute. That was the lone goal until Manolo Gabbiadini equalized in the 89th when goalkeeper Michael Agazzi let the ball trickle through his legs.
Daniele Conti restored Cagliari's lead in the first minute of added time with a splendid free kick and Gabbiadini scored again with a deflection two minutes later.
In Genoa, the closest either side came to scoring came when Genoa's Thomas Manfredini hit the crossbar with a header from a free kick in the 76th.
Livorno, which finished third in Serie B last season, is just two points behind league leaders Napoli and Roma.
Udinese's attempt to equalize fell short when defender Dusan Basta hit the crossbar with a long shot in the 72nd.
On Sunday, Napoli's perfect record will be put to the test at the San Siro against AC Milan. Roma, which also has three wins in three matches, faces Lazio in the capital's derby. And two-time defending champion Juventus hosts newly promoted Hellas Verona.