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The win secured a top-20 finish at the World Cup and was the side's first win over Turkey.
The win was built on a wide-reaching offensive effort, with Rob Loe enjoying his best game of the tournament, named man of the match for a display that included one-handed put back dunks, three rebounds, four assists and his trademark shooting from deep, ending with 17 points.
The support cast was extensive. Isaac Fotu posted 17 points and five boards, and young Finn Delany came alive for a breakout performance at this level with 12 points and seven rebounds.
Webster had 12 points, three boards and three assists, while the tournament's leading scorer, Corey Webster, also had 12 and dished off five dimes as he was often shut down by the Turkish defence.
Head coach Paul Henare was proud of his whole roster.
''I am a little bit lost for words, not just for that result but in the greater scheme of things, what that says about our programme and what we have done throughout this tournament.
''I am so proud of this team, for their fight and the commitment to play the way we want to play. To be able to do it on this stage is just unbelievable,'' he said.
Delany was huge for the Tall Blacks, grabbing vital rebounds and dunking at will over the Turks.
''He was amazing. The energy he played with was at a time when we needed it, at a time when we could sense a shift in momentum with the Turkish guys - you could see the fatigue hitting them. He saved his best for last. I am really happy for him.''
Henare was also pleased that the game plan paid dividends, not with a gallant loss, but with a quality win over a quality team.
''Let's not dance around the fact we didn't achieve our goals, but we still had plenty to play for, against a top 10 team in the world in what is the first time we have ever beaten Turkey, as far as I can remember. There is just so much there.''
New Zealand came in with a world ranking of 38 and will officially finish 19th at the tournament with three wins and two losses, as one of four pool winners in the classification stage. Just points differential separated it from other winners Nigeria and Germany.
The side will now turn its attention to Asia Cup qualifying and the Olympic repechage tournaments next June, for which venues are yet to be decided. In all, 24 teams will play in four tournaments, with just the tournament winners booking a place in Tokyo.