Price and Classic Moet recorded the fastest time in heavy, treacherous conditions, the course badly affected by poor weather in recent days.
They clocked 10min 48s, to incur only four penalty points.
''I haven't had her long and I was just planning to go out and keep asking the questions," said Price of Classic Moet. "She is light on her feet, very courageous and with a big heart."
Price tried to find new ground to run the petite black mare on, and her only hairy moment came when she lost a rein and had to take the longer option at the last water jump.
Nicholson on the experienced Nereo was second fastest to ensure he's in the final day mix.
However the course took its toll on the other New Zealanders.
Mark Todd and Leonidas II parted company at the last water jump near the end of the track.
"It is very disappointing," Todd said. "We knew that was a fence we had to respect,,,but he still had plenty of running in him."
Tim Price and Wesko looked to be in good form until tiredness forced the horse to stop near the end.
''There was just nothing left," said a disappointed Price said.
Lucy Jackson and Willy Do was riding the round of her life until they too parted company at the same fence as Todd.
"I am just gutted," she said. "You can't get away with even the smallest mistake at this level. Willy Do deserved to be in the glory house, and I am so proud of his heroic efforts."
Jock Paget and Clifton Promise had a run out at the fifth fence and retired not long after.
The inability of Todd, Paget and Tim Price to complete the course did for New Zealand's team chances, where at least three combinations are required to finish the event. Jonelle Price and Jackson are competing as individual representatives.
Germany leads the teams event on 177.9 points, from Britain on 186.8 with Australia third on 226.8.