Price, part of the bronze medal-winning team at the London Olympics in 2012, jumped from 22nd to the top of the leaderboard after a cross country effort.
They were the fastest combination on course, going over time by just a second and picking up 0.4 penalties to finish the day on 28 penalty points.
Overnight leader Oliver Townend of Britain on Ballaghmor Class picked up 7.2 time penalties to also finish on 28 but in second place as Price was closest to the optimum time.
Of the 10 Kiwi combinations, seven came home clear.
Mark Todd is in sixth place aboard Kiltubrid Rhapsody on 33.4 penalty points, and 10th on Leonidas II with 36.3.
Defending champ Andrew Nicholson and Nereo are in 12th on 37.5, with Tim Price 14th on Ringwood Sky Boy with 38.2.
Caroline Powell was clear with both her horses and sits in 33rd spot with On the Brash on 65.1 and trailblazer Up Up and Away, who sits in 36th spot on 67.7.
First-timers Virginia Thompson and Star Nouveau picked up 11 faults to finish on 70.2 in 39th, with Dan Jocelyn and Dassett Cool Touch on 81.4 in 44th. Andy Daines and Spring Panorama were eliminated late in the course.
But the day belonged to Jonelle Price, who is originally from Nelson.
"She is some horse at cross country," she said of Classic Moet. "Her speed is quite phenomenal. There really is no other like her and to show that time and time again is really special."
"We certainly dug ourselves out of that hole and to get that close to the time after having to take the long option was really remarkable.
''We were 16 seconds down at one stage. I owe it all to her. She is some mare and comes into her own on a day like that."
Todd figures the hold up he had on course with Kiltubrid Rhapsody probably didn't do the horse any harm.
"He hasn't got a lot of thoroughbred in him and he was starting to feel a little laboured going up that avenue, so I was nursing him a bit," said Todd. "It has been a great day and my horses have gone really well."
Nicholson said riders needed to work all the way around the course.
"I was relieved I was on Nereo," he said. "Once you leave the start box you don't notice (the crowd) – you don't listen, you don't watch, you just look at the jumps and do what you do. The ground out there is good for horses but makes them tired."
The showjumping phase will be a pressure cooker with not even a rail between the top four, and less than two in the top nine.
