Elsewhere, Papua New Guinea scored 10 tries to swamp Wales 50-6 in Port Moresby and Fiji hammered the United States 58-12 in Townsville.
The second-ranked Kiwis, tournament winners in 2008, held a 10-4 advantage at half-time but ripped open the fifth-ranked Samoan defence with five tries.
Scrum-half Shaun Johnson finished with 14 points from a try and five goals with other tries scored by Jordan Rapana, Brad Takairangi, Kodi Nikorima, Isaac Liu, Roger Tuivasa-Sheck and Nelson Asofa-Solomona.
Tuivasa-Sheck (202 metres) and Asofa-Solomona (181 metres) ran the most metres in the game.
New Zealand’s win in Pool B was soured by an apparent serious leg injury to Gerard Beale.
Brisbane Broncos fullback and skipper David Mead scored a hat-trick of tries as Papua New Guinea crushed Wales in their tournament opener in Pool C.
The 16th-ranked Kumuls thrilled their capacity home crowd with 10 tries to one in a dominant performance over the number 9-rated Wales.
Wales wilted in the stifling tropical heat and struggled with field position as the Kumuls enjoyed 62 percent possession.
The Welsh finally got on the board as the full-time siren sounded with Regan Grace scoring off a Matt Seamark kick.
Fiji totted up 11 tries in routing the United States to take early control of Group D.
The seventh-ranked Fijians showed USA no mercy and were seven tries to one up by halftime, before running in another four tries to post the tournament’s biggest win so far.
NRL stars Kevin Naiqama and Suliasi Vunivalu scored two tries each, while Gold Coast Titans superstar Jarryd Hayne launched his World Cup by scoring next to the posts following a mid-field break by Akuila Uate.
Fiji’s big win may have come at a cost, with prop Kane Evans coming off clutching his wrist after scoring a first-half try.
