Contrary to the final result, it was Japan who scored an early goal in the fourth minute through Akiko Kato.
New Zealand equalised within a minute through a open play strike by Petrea Webster.
The Black Sticks raised the tempo of the contest in the second half as Sophie Cocks, Kisten Pearce and Gemma Flynn scored in open play and captain Anita Punt converted a penalty corner to ensure their place in the semifinals.
Meanwhile in the first quarterfinal of the day, World Cup silver medalists Australia, who lost their preliminary match to New Zealand, were made to work hard by lowly-ranked Italy.
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Both Australian goals came through penalty corner conversions by Jodie Kenny (21st minute) and Anna Flanagan (40th).
Australia now await the winner of the quarterfinals between World Cup and Olympic champions The Netherlands and India, to be played later today.
Three top teams from this World League Semifinals will qualify for the 2016 Rio Olympic Games.