They headed Martin Laird by one stroke, while fellow Briton Lee Westwood began slowly with a 73, barely a week after being part of the victorious European Ryder Cup team.
Defending champion Jimmy Walker, who played on the losing American team at Gleneagles, started even more poorly with a 75.
His team mate Hunter Mahan was considerably better with a
respectable 70, while Matt Kuchar carded 71.
The 28-year-old Bae, a 12-times international winner before joining the PGA Tour, captured the Byron Nelson Championship in 2013, but is coming off a mediocre season in which he finished 122nd in the ranking.
He put all that behind him, though, with five birdies on his outward nine.
Gonzales, who played on a crisp morning that quickly warmed to an ideal autumn day, matched Bae’s seven birdies and one bogey.
“It's definitely a confidence builder getting out here and starting that way,” Gonzales, a third-year tour player from Washington State, told reporters.
“I really feel good about it because I don't think I was as sharp as I could have been, but as far as ball‑striking, I scrambled well and got up‑and‑down.
“When I did miss fairways, I missed them in the right spot. There's definitely a lot of room to improve, but I’m pleased with the way I've started.”
Australian Jarrod Lyle, in his first tour event since overcoming leukaemia for the second time, double-bogeyed the 17th hole for a 72.
“It was obviously a little disappointing to finish that way, but even par, I haven't shot myself in the foot, so it's a good start to the week,” Lyle said.
(Reporting by Andrew Both in Cary, North Carolina; Editing by Ian Ransom)
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