And the Black Sticks had also showed true grit to reel in a two goal advantage in the second period with goals to Glynn (42nd minute) and Michelsen (59th minute).
Japan regained their advantage with just over ten minutes on the clock before Glynn's late strike.
Though the two teams have not clashed often in international competition, the Black Sticks have enjoyed dominance over Japan in recent years, with the Asian side winning just one of five clashes in 2011.
However Japan had been the big improvers of this week, impressing against Germany in their quarter final before shocking Korea in extra time on Saturday.
For today's game there was heavy rain in the morning but clouds had cleared for the match. Earlier the New Zealanders had been forced to warm up on the road outside the stadium, jogging past several bemused locals and policeman.
After being fast out of the blocks in their first two matches, for the fourth game in succession New Zealand conceded the first goal.
It was an innocous strike, with young defender Rhiannon Dennison letting the Japanese striker Akane Shibata drift in front of her and tap it past a stranded Sally Rutherford in goal in just the third minute.
It was almost a carbon copy of the first goal against Holland, with the inexperienced Dennison being caught out on that occasion too. Coach Mark Hager obviously wanted pace at the back but it still seemed a gamble to start with the youngster.
It was a flat start from the Black Sticks, with coach Mark Hager constantly calling for more energy from the team. Japan forced four penalty corners in the first 20 minutes and New Zealand was playing with fire, as Japan had been the most deadly from the line before this match.
Despite, Hager's remonstrations, New Zealand was still guilty of waiting for the ball to come to them and were consistently caught flat footed by the pacy Japanese.
It was no surprise when Japan doubled their lead in the 15th minute, as the Black Sticks were caught ball watching in the area and Izuki Tanaka was left alone at the far post.
The Black Sticks had failed to carve out a single clear cut chance in the first period but came out fired up in the second spell after some choice words from coach Hager.
From the renewed effort came the reward. In the 42st minute Katie Glynn skillfully deflected home a lofted shot from Charlotte Harrison. Eleven minutes later and New Zealand drew level. Before their third penalty corner of the half, Hager called a variation and it worked a treat as Stacey Michelsen deflected home at the near post after a Kayla Sharland strike.
But from one of their few attacks of the half, Japan regained the lead with a well worked goal to Kaori Fujio in the 59th minute.
The Black Sticks pushed everyone forward in the last ten minutes and their courage paid off with Glynn's late strike.
The final between hosts Argentina and Great Britain is scheduled for midday (NZT) today, with Holland to meet Germany in the play off for third and fourth.
New Zealand 3
Japan 4
Halftime: 2-0
