Instead of having the opportunity to take a 3-2 lead, New Zealand fell behind - somewhat ironically from a penalty corner - but rallied, continued to force the pace and five minutes from time snatched the equaliser.
Stephen Jenness pounced on goalkeeper Jacob Stockman's clearance and swatted the ball home.
With 3m 30s to play, the Dutch went upstairs but their plea was also turned down. From the restart, Couzins lost possession, Teun de Nooijer swooped and fired the ball in and Bob de Voogd's deflection beat gallant Black Sticks goalkeeper Kyle Pontifex for a 4-3 lead.
As he had done against the Dutch earlier in the Owen G. Glenn FIH Champions Trophy tournament, McLeod called Pontifex to the bench and added an extra outfield player in the hope of snatching another late equaliser.
The plan did not work and the Dutch, with no goalkeeper to beat, scored their fifth goal in the last minute.
The visitors had created early chances, and although Pontifex was at his best, the pressure told. In the sixth minute New Zealand turned the ball over, the Dutch broke quickly and Jeroen Hertzberger fired in a reverse stick shot which deflected off Pontifex's pads across the line.
New Zealand then took the initiative, asking questions of the Dutch defence, and were deservedly rewarded with a 19th minute equaliser when Nick Wilson scored from a goalmouth scramble.
By halftime there was another exchange of goals for 2-2 in a match which flowed back and forth.
Blair Hopping marshalled the Black Sticks defence well and set up a number of promising attacks with defence-splitting long balls often aimed at Phil Burrows, who turned in another non-stop effort - a day after he had been forced off with blood streaming from a nasty gash above his eye.
In almost exactly the same spot on the pitch where some years ago McLeod was felled in a similar incident, Burrows departed to have 15 stitches inserted. "Three more than I had," joked McLeod.
The coach was philosophical after the loss.
"The guys are really disappointed. They have had a fantastic tournament. They are getting closer and closer to the world's elite but that does not hide the disappointment they feel.
"We were up against the fourth-best team in the world. We are three places back on those rankings but you would not know that. Looking ahead [to the London Olympics] we are sitting in good position. We have gained confidence against these teams."
Dutch coach Paul van Ass paid tribute to the New Zealand team and the tournament organisation.
"Given the crowd support we had to play 12 again," said van Ass. "We were disappointed not to reach the final but I said to my players they had to go out and try to win bronze. That is often better than playing in a final and losing gold."
The Black Sticks would have settled for either.
