Morris Hatalsky capped the round with consecutive birdies and was two strokes behind Morgan in the Champions Tour's first full-field event of the year.
Four rookies were among the group at 68, including John Cook, seeking his second victory in his fourth start on the 50-and-over circuit. He was joined by fellow rookies Fulton Allem, Bernhard Langer and Phil Blackmar.
Tom Kite, Jim Thorpe and Donnie Hammond also were at 68.
The 61-year-old Morgan, who struggled at last week's MasterCard Championship, quickly moved up the leaderboard during the middle holes. Starting on No. 8, Morgan went birdie-eagle-par-birdie-eagle to reach 8 under.
'It was pretty fast and furious for a while,' he said.
Both eagles came on par 5s. He chipped in from 35 feet near the front of the green for the first eagle and sank a 35-foot putt on the other.
It was Morgan's best run since he carded an eagle and double eagle in the first seven holes of the 2001 Instinet Classic.
Morgan got up-and-down to save par on No. 14. He looked at the leaderboard on 16th and noticed he had built a nice cushion and had thoughts of a possible third eagle and reaching 10 under.
He lost a stroke when he was caught between clubs and three-putted the par-4 17th from 30 feet.
'I wasn't thinking well and I let that one get away from me,' said Morgan, coming off a 37th-place tie in the 41-player field at Hualalai. He was just a stroke out of last place and one of five players who failed to break par in the winners-only event.
Morgan said he didn't practice much in the offseason and felt a little rusty at Hualalai, which plays much easier than Turtle Bay.
'Hopefully, my game will come around a little bit as I go forward,' he said. '(But) I don't know if I could improve on this round.'
Morgan, who won the 2007 Wal-Mart First Tee Open for his 25th Champions Tour victory, is making his fourth start at Turtle Bay, where he tied for 28th last year after closing with a 65.
'I haven't played as well as I would've liked at this golf course,' he said. 'It's always windy it seems. It's always blustery conditions. I was kind of surprised with my round today.'
Conditions at the oceanside Palmer Course were relatively calm Friday. Possible showers were expected for the weekend.
The group at 69 included Ben Crenshaw, Dana Quigley, Scott Simpson, John Jacobs, Bobby Wadkins, Mike Reid and Thailand's Boonchu Ruangkit.
Defending champion Fred Funk, who ran away with a record 11-stroke victory a year ago, opened with a 70, five strokes off the pace.
The 51-year-old Funk is seeking a Hawaiian sweep with his two-stroke victory over Allen Doyle at Hualalai. The victory came after he opened the year by tying for 25th in the PGA Tour's Mercedes-Benz Championship and tying for 10th in the Sony Open.
Funk, who had been dealing with a sinus infection, bogeyed No. 13, his first bogey in 67 holes at Turtle Bay.
Last year, Funk had the most-lopsided victory ever in a 54-hole Champions Tour event, finishing with consecutive 8-under 64s for an 11-stroke, wire-to-wire win. He had a tournament-record 23-under 193 total.
Six-time Turtle Bay winner Hale Irwin opened with a 72, as did 2006 winner Loren Roberts.