Ciro Ferrara's side lead the table with a maximum 12 points from four games but they again had to thank goalkeeper Gianluigi Buffon for the result as much as the goalscorers.
Italy striker Iaquinta, who netted in the lacklustre 1-1 draw with Girondins Bordeaux in the Champions League on Tuesday, headed in Mauro Camoranesi's cross after eight minutes.
"Definitely it's a good period for me," Buffon told Sky television. "We've won fairly comfortably but Livorno had a good game. We move on with optimism, knowing we can improve."
Udinese's Antonio Di Natale had an effort wrongly ruled out for offside in the first half and was denied by a smart save by Morgan De Sanctis in the second when Marek Hamsik also missed a golden opportunity for the hosts.
Napoli's stadium manager was arrested on Friday after a raid at the Stadio San Paolo discovered 200 kilograms of illegal fireworks, which police believe were destined to be used by hardcore home fans.
Champions Inter Milan visit Cagliari and AC Milan entertain Bologna without 'flu victim Ronaldinho in Sunday's main set of matches while AS Roma welcome Fiorentina.
