India pulled a goal back in the 12th minute through Danish Mujtaba before Wellington's Joel Baker celebrated the fourth goal just before half-time, sweeping home Arun Panchia's pass high into the roof of the net.
India fought back hard at the start of the second half and reduced the deficit twice through Sardar Singh and Ravi Lal to make it 4-3 to New Zealand before Jenness added his second and New Zealand's fifth with a clever reverse stick flick in a crowded circle in the 25th minute.
New Zealand were denied a sixth when captain McAleese converted a penalty only to have the umpire disallow the goal before Jenness completed the first ever Super Nine hat-trick, when he was released by Andy Hayward's accurate pass to fire home at the second attempt.
This new competition, a fast-paced, action-packed nine-a-side variation of the traditional game, which could be seen almost as hockey's version of 20/20 cricket, played to packed audiences in Perth.
In the other game played last night, Australia edged Pakistan 3-2. The Black Sticks play World and Commonwealth champions Australia at 7.30pm (Perth time) today with Pakistan meeting India in the second match.