His was nine-under par through his first 14 holes but marred his excellent card with a bogey on his last hole, the par four ninth.
Dunedin's Mahal Pearce was on track to tie with Zwart when he made four straight birdies from 14 to 17 but a bogey on the 18th hole had him one short on 65.
Tauranga's Jared Pender was impressive with his seven-under par round of 65, seven birdies and no errors.
Turning through nine three-under the card, he reeled off four more birdies in a row from 10 through 13, and was a bit disappointed to only par it home from there.
Aucklander Joonsang Chung and Richard Lee, of North Harbour, were tied fourth on 66. Chung was off to a fast start, making birdies on his first three holes, got to seven-under par after 14 but made bogey on the par-four 15th hole.
Lee was also in with a big chance when he got to seven under the card through 13 holes, but a bogey on 17 had him come up short of the leaders.