Without an exemption, Goodes had to qualify for the tournament on Monday in North Carolina and matched his best round since joining the Champions Tour in 2006.
Goodes' final birdie - on No. 13 - moved him to 7 under during a bogey-free round after Bean had taken the lead into the clubhouse. Two holes earlier, Goodes holed out from a bunker for another birdie.
"It's fun to play a good round, and I know it means absolutely nothing right now," said Goodes, who has had to qualify for each of his six tournaments this year and has managed only one top-25 finish. "I hope I play two more.
"I may try to play tomorrow just like I did today, which was try to make smart decisions and hit aggressive shots. That was kind of my mind-set going into today and I hope that's what it will be the next two days."
Bean also is an unlikely leader. His only top-25 finish this year came when he tied for fourth at the Liberty Mutual Legends of Golf on April 27 and he has one win in 130 Champions Tour events.
"I hit it close all day. I don't know if I had a shot outside 20, 25 feet all day hitting into the green," said Bean, who has two daughters living in Birmingham.
Two-time defending champion Brad Bryant opened with a 72 after bogeys on the final two holes.
Bob Charles, Mike Hulbert and Walter Hall were three strokes behind Goodes and Bean, while Denis Watson was among six players four shots behind. Watson won the FedEx Kinko's Classic on May 4 for his second victory of the year and fourth in two years. The 72-year-old Charles bettered his age for the eighth time on the Champions Tour.