Scott, who hit 14 of 18 greens in regulation, had six birdies and a bogey at Silverado in Napa, California, where he finished the day tied atop the leaderboard with American Andrew Landry.
The duo were one stroke in front of Italy's 2018 British Open champion Francesco Molinari and American Matthew NeSmith.
Scott teed it up in this early event of the US tour's 2019-2020 season with his eye on the Presidents Cup match play tournament at Royal Melbourne in December.
The 39-year-old Aussie, who took time off after finishing tied for fifth at the Tour Championship in August, goes into the season seeking a first title since 2016, when he won the Honda Classic and the WGC event at Doral.
He had runner-up finishes at Torrey Pines and the Memorial tournament this year, and remains confident he can return to the winner's circle before too long.
"I just need to keep the intensity up," Scott said. "I feel like I've had points like this in my career before - most obvious to me was in 2012, where I played great all year and didn't win.
"Eventually, I won a tournament late in the year in Australia just because I kind of kept up the intensity and kept pushing forward. So I kind of feel like I'm in the same place now."
Scott, playing Silverado for the first time, found it to his liking.
"I actually really enjoy this kind of tighter, smaller style courses," the former Masters champion said.
"A lot of the holes remind me of a lot of golf in areas of Australia, too, with the big trees. I know they're oaks here, but there's some eucalyptus around this area. Looks similar to Australia, so I feel quite comfortable out there."
In addition to his eagle bomb, Scott rolled in a 32-foot birdie at the 14th.
"I've been putting really nicely this whole year," he said. "I've been rolling some long ones in, which is obviously very helpful no matter what they're for, par or birdie or eagle. But I felt really solid on the greens, so I'm just going to try and keep that going."
Landry matched the early target set by Scott, seizing his share of the lead with a 20-foot birdie at the eighth - his 17th hole of the day.
Leading first-round scores on Thursday in the US PGA Tour Safeway Open in Napa, California (USA unless noted, par 72):
65 - Adam Scott (AUS), Andrew Landry
66 - Francesco Molinari (ITA), Matthew NeSmith
67 - Cameron Champ, Adam Long, Chris Baker
68 - Cameron Tringale, Corey Conners (CAN), Bryson DeChambeau, Rob Oppenheim, Tyler Duncan, Morgan Hoffmann, Adam Hadwin (CAN)
69 - Sepp Straka (AUT), Nick Watney, Bud Cauley, Chez Reavie, Kim Si-woo (KOR), Aaron Baddeley, Lanto Griffin, Vince Covello, Zhang Xinjun (CHN), Nick Taylor (CAN), Talor Gooch, Patrick Cantlay, Chase Seiffert