Fiji threatened a major upset in Newcastle, leading New Zealand 12-4 after 30 minutes in their World Cup debut.
Losana Lutu and Sienna Laing had scored for the Bulikula, but Zahara Temara's late penalty and Leianne Tufuga's try secured an 18-12 win for the Kiwi Ferns.
New Zealand will meet France in Christchurch in Round 2, while Fiji travel to Port Moresby to face Papua New Guinea.
In Port Moresby, Naomie Kelly scored four tries as the PNG Orchids began their campaign with a 58-4 victory over France.
Craig Sandercock's team scored 12 tries to France's one in a dominant display.
England also delivered a strong attacking performance, defeating Wales at Perth's HBF Park.
Player of the match Isabel Rowe scored 26 points, equalling the record for most points by an English woman in an international match.
Debutant centre Connie Boyd scored a hat-trick, and Anna Davies also crossed three times.
The result set up an England clash with defending champions Australia in the tournament's second week.
Australia opened with a 40-0 win over Samoa, led by five-eighth Jocelyn Kelleher's impressive debut.
Kelleher's kicking troubled Samoa, and she also made a line break and set up a try.
Seven Australians scored tries as the Jillaroos built a 28-0 halftime lead and completed a composed victory.