The game started with the temporary suspension of New Zealand's Don McLeod for a punch on Sean Kerly, his former Southgate team-mate.
He was the first of four New Zealand players to be given temporary suspensions. Britain's Rob Hill and Steve Batchelor were also sent to the sin-bin.
On the field, Britain got off to a good start with one goal by Hill, from a penalty corner, and another by Jon Potter, from a penalty stroke, inside the opening 10 minutes.
New Zealand fought back strongly, however, taking advantage of poor British defensive play, to score at penalty corners through Craig Russ and McLeod, back again after the briefest of suspensions - just five minutes for what many people considered a red-card offence.
The controversial nature of the game intensified after the interval when, in the 40th minute, Britain's Sam Martin, making a British record 229th international appearance, was shown the red card - permanent suspension - for allegedly deliberately hitting David Grundy with his stick.
Yet there appeared from the stand to be no aggressive contact, as confirmed by both player and coach afterwards. Television pictures were inconclusive. However, Martin is now automatically suspended from Britain's game against Spain.
Britain's winning goal came 10 minutes from time, with New Zealand reduced to nine men against Britain's 10. Rob Thompson, who had worked tremendously hard, enjoying one of his best international appearances, bored his way through the Kiwi's defence. His shot took a deflection, falling to Batchelor, who juggled with the ball before lobbing it over the goalkeeper for a rare goal.
GREAT BRITAIN: S Rowlands (Havant); S Martin (Holywood 87), P Bolland (Hounslow), J Potter (Hounslow), J Laslett (Teddington), R Hill (Havant), S Batchelor (East Grinstead), J Shaw (Southgate), S Kerly (Canterbury), R Clift (East Grinstead, capt), R Thompson (Hounslow). Substitutes: S Nicklin (Slough) for Shaw, 36; R Garcia (Havant) for Clift, 36.
NEW ZEALAND: I Woodley; A Thornton, D McLeod, P Miskimmin, J Smith, B Leaver, D Grundy, J Radovonich, P Daji (capt), C Russ, G Russ. Substitutes: S Hobson for Leaver, 43; U Parag for G Russ, 58.
Umpires: R Wolter (Ger) and D Prior (Aus).
Germany will play Australia in the Olympic final after beating Pakistan in extra time 2-1 coming from behind with a penalty stroke and penalty corner goals from Carston Fisher. Australia beat the Netherlands 3-2 with goals from Paul Lewis, Lee Bodimeade and Ken Wark. Both Dutch goals came from Floris Bovelander.
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