Owen chipped in for birdie on the 11th, his second hole, and carded five more in a flawless six-under-par round at Sea Island Golf Club.
That left him two shots off the pace set by American duo Bud Cauley and Marco Dawson, with US Ryder Cup captain and tournament host Davis Love one behind Owen after a 65.
"I'm working really hard this week and it's starting to pay off," said Owen, who had to go through the qualifying school to get back on the PGA Tour.
The Mansfield golfer is 93rd on the money list after playing last season on the second-tier Web.com Tour, when he admitted he was very disheartened with his game.
"I struggled the last four, maybe five years," Owen said. "This year I just played really solid. I've putted better, I've holed out better. And (hopefully) there's still more to come."
Strong iron play was the key to Owen's round, with his longest birdie putt coming from just 11 feet.
"If the wind blows and the sun comes out this afternoon those greens could get really quick," Owen added.
"You've got to hit golf shots. You've got doglegs either way. You've got to hit fairways and place the iron shots in a position where you can have a putt for birdie."
Love admitted he was in need of some extra stimulation after the rigours of being Ryder Cup captain at Medinah and tournament host this week.
"The only adjustment I've made is more Red Bull to keep my energy up," Love told PGATour.com.
"After the Ryder Cup I've been playing these last two weeks and I'm ready to play. The responsibilities, the parties and all that are a lot of fun, but when I get up in the morning I can tell I'm not getting a whole lot of rest.
"But I'm feeling good. I'm excited to play."