Number 10 Tiaan Falcon slotted eight from nine goalkicks for 19 points.
The pack presented a solid scrum and were energetic around the track, but they are not the only eight to struggle with legally combating a lineout drive, from which the Italians reaped the benefit of one try to hooker Alberto Rollero.
They had, in fact, opened the scoring within the first two minutes, when Ennor threw a pass that fullback Simone Cornelli intercepted and ran 70 metres for the try. Italy's pack was big and committed, but they offered little on attack, whereas New Zealand continually punched holes out wide.
However, Italy did score four tries, thus securing a bonus point that may be crucial, when they face Scotland in the next round.
New Zealand will be pleased they were more efficient than they were against Scotland and they look to be humming on attack. They just need to tidy up their defence and lineouts.
Captain Luke Jacobson was sinbinned.
Coach Craig Philpott was not unduly concerned.
"It's good to play on a sunny day and good grass, and the boys enjoyed themselves," he said. "Defensively, we want to be better, but we also want to play and sometimes, it's a bit of risk and reward."
In the other Pool B match, Scotland edged Ireland 32-28 to knock the latter out of semifinal contention.
New Zealand will now face Ireland on Thursday night (NZT), having waited 12 months to gain revenge on the side that knocked them out of the 2016 event.
New Zealand 68 (Caleb Clarke 2, Will Jordan, Orbyn Leger, Jona Nareki, Braydon Ennor, Pouri Rakete-Stones, Tamati Tua, Adrian Choat tries; Tiaan Falcon 5 con, 3 pen, Leger 2 con) Italy 26 (Simone Cornelli, Niccolo Cannone, Michele Lamaro, Alberto Rollero tries; Filippo Di Marco 3 con) HT: 39-21
