In the opening match against the Kenyans, Sonny Bill Williams' sister went one up on her famous brother.
On a day where rugby returned to the Olympics for the first time in 92 years - and women's rugby appearing for the first time - Niall Williams scored one of the New Zealanders' eight tries in their strong performance. It meant she is on the scoreboard ahead of Sonny Bill in the Williams household boasting stakes. The men's tournament starts later this week.
McAlister's first try in the second pool match gave New Zealand a 12-0 lead at halftime against Spain.
Tyla Nathan-Wong then added a third shortly after the break, before Maria Casado scored for Spain - the first points New Zealand have conceded in 24 minutes of play.
Beyond McAlister, Woodman and Williams, New Zealand also scored tries through Huriana Manuel and Gayle Broughton in the first game.
Nathan-Wong showed she could be a vital cog by kicking five of six conversions and Kelly Brazier one of two.
New Zealand led 21-0 at halftime against the Kenyans.
In other matches, gold medal favourites Australia went one point better than New Zealand by trouncing Colombia 53-0, Britain defeated Brazil 29-3 and France won the opening match, downing Spain 24-7.