“Just made some really good swings and putter got hot, as well.”
The tournament winner receives US$1.53m ($2.72m) while a victory could rocket Kobori into contention for a top 10 spot on the DP World Cup which would earn a PGA Tour card.
Fellow Kiwi Daniel Hillier is two shots back in a share of 13th after shooting a 66.
Lowry and Fleetwood, both previous winners of the event, were drawn in a group that also included a third Ryder Cup player, Rasmus Hojgaard.
“It was nice,” said Lowry. “I was pretty excited when I saw the group, my pairing today, and it was nice to go out there with the boys.”
Fleetwood carded eight birdies and no bogeys, while Lowry fired nine birdies and dropped a single shot.
“Something about me and Tommy,” the Irishman added. “I just like playing with him, your friend, and really good player too.
“And you kind of feed off each other. It was nice.”
Fleetwood agreed.
“I’m so close to both the guys, Ryder Cup teammates, played with Rasmus, who I’m close with last week. It was great,” the Englishman said.
“You focus on your own game,” he added. “It shouldn’t make that much difference but definitely when you’re in a comfortable pairing or group it’s nice. It’s helpful.”
Dane Hojgaard ended the round in a chasing pack of seven, one shot off the lead.
Another Ryder Cup player, Ludvig Aberg, made a hole-in-one on the par-three eighth and finished the day two shots back.
Rory McIlroy opened with a four-under 68 to sit in a share of 27th.
– With AFP