Funk said he didn't know how much opening the season on the PGA Tour actually helped. Doyle said there was no doubt it helped Funk.
"I'm sure that helps. He was probably coming here, feeling very good about his game," Doyle said.
Jay Haas, seeking a record third straight money title and player of the year award, closed with a 67 to tie for third with Bernhard Langer (65) at 17 under.
First-round leader Tom Purtzer had a 69 to finish fifth at 16 under.
The wind was down most of the day at Hualalai until late in the afternoon when it changed directions and shook the palm trees and most of the players, except Funk.
Funk made his move on the back nine. He tapped in for birdie on the par-5 10th to move to 17 under and trim Doyle's lead to two strokes. Doyle lost a stroke on the next hole when he missed the green short and his chip died 10 feet from the hole.
Funk tied Doyle for the lead by sinking a 26-foot birdie putt on the par-3 12th.
"He's got a four-shot lead and I was just saying, 'Let's have a good tournament regardless of what Allen's doing,' and all of a sudden I got on a little roll," Funk said.
The 59-year-old Doyle, seeking his 12th Champions Tour victory and his first since the 2006 U.S. Senior Open, parred his final five holes.
Doyle, who dropped 20 pounds in the offseason, said his round was encouraging after a poor ending last season.
He birdied three of his first four holes and started to pull away. Funk, meanwhile, was having trouble early off the tee.Doyle started the round by holing a 12-foot birdie and opened up a four-stroke lead over Purtzer and Funk when he chipped to a couple inches for birdie on the 551-yard seventh.
"The momentum was totally Allen's at the beginning of the day," Funk said.
After bogeying No. 2 because of a tee shot in the left rough, Funk got a couple consoling pats on the back from his 12-year-old son Taylor as they walked together to the third tee.