The 51-year-old Funk, coming off a 10th-place tie last week in the PGA Tour's Sony Open, finished with a 21-under 195 total for his third Champions Tour victory in 14 starts and his second title in Hawaii in two years.
Doyle, who blew a four-stroke lead, had a 68.
Funk screamed 'Yes!' and raised his club in the air after he chipped in from 20 feet on No. 17. He then holed a 7-foot birdie putt on the 54th hole, after hitting a spectacular shot out of the white-sand bunker from 149 yards.
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 until late in the afternoon when it changed directions and shook the palm trees and most of the players, except Funk, who earned $300,000 in the first of 29 Champions Tour events.
Funk opened the season on the PGA Tour, tying for 25th in the Mercedes-Benz Championship and tying for 10th at Waialae. He will now head to Oahu to defend his title at the Turtle Bay Championship, which he won by 11 strokes last year.
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. Most of the leaders birdied the hole except Doyle, who missed his approach to the right and ran a chip past the hole.
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. Funk nearly holed his second shot on the 13th from 94 yards. He tapped in for birdie.
The 59-year-old Doyle, seeking his 12th Champions Tour victory and his first since the 2006 U.S. Senior Open, fought off the challenge by making a 21-foot putt for birdie to keep the pace.
Funk missed short birdie putts on Nos. 14 and 15 that would've given him the outright lead. But he was able to apply more pressure on Doyle, who parred the final five holes.
Doyle, who dropped 20 pounds in the offseason, was relaxed and loose as he walked the front side. The New England native discussed the Patriots' victory over the San Diego Chargers with his caddie.
Doyle birdied three of his first four holes and started to pull away.
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.
Defending champion Hale Irwin closed with a 68 after two rounds in the 70s. He tied for 30th in the elite field of 41 with a 6-under 210 total.
The 62-year-old star, who has nine official victories in Hawaii, beat Jim Thorpe and Tom Kite last year by five strokes for his tour-record 45th victory.
Lee Trevino (74), the oldest in the field at 68 and one of seven Hall of Famers in the field, was the only golfer above par and finished in last place.