Skipper Brian O'Driscoll also crossed for the Irish while Ronan O'Gara added 16 points with the boot, Mirco Bergamasco's two penalties all the Italians had to show for their efforts.
The Irish remain unbeaten in the tournament while the Italians will be on the next plane home but Kidney insists there is plenty still to do.
"This is probably phase one for us, we wanted to get out of the pool, that was a massive thing for us so this was an all or nothing game against Italy," he said.
"We played it like a final and we're just glad to have made it out the pool now.
"The first-half was pretty nip and tuck but it always is in Ireland v Italy matches and it's a case of taking the breaks when they come your way.
"Tommy (Bowe) got a bit of an opening and we managed to finish it well and that was important because it gave us a bit of daylight from then on."
The head coach also found time to highlight the magnificent Irish support who made Dunedin feel like Dublin for large parts of the encounter.
He added: "Times are difficult in Ireland economically so the fact that they have come down all this way to watch us is great, we're just so happy that they're enjoying themselves and having a good night out."
O'Gara, preferred to Jonathan Sexton at fly-half, settled early Irish nerves with a penalty in the seventh minute but moments later Italy were level through the boot of Bergamasco.
In a tight first half two more O'Gara penalties, either side of another Bergamasco effort, meant the sides went in at the break only 9-6 ahead, Bowe having had a try ruled out for a forward pass.
But after the interval it was a different story and O'Driscoll streaked clear in the 47th minute to touch down under the posts after Bowe had sliced through the Italian defence.
O'Gara's reliable right foot kept the scoreboard ticking over before Earls went over in the corner for his side's second try after fantastic work from Gordon D'Arcy in the build-up.
Sexton then came on in the final quarter for O'Gara and added a penalty of his own before Earls grabbed his second and Ireland's third try of the night, touching down after a fine initial break by replacement Andrew Trimble.