Jim Thorpe, Joe Inman and Bruce Fleisher share fourth place at 3-under-par 69.
Strange, whose last win on the PGA Tour came at the 1989 U.S. Open, got up and down for birdie from a bunker at the par-5 second. He hit a 7-iron to 30 feet to set up birdie at the 188-yard, par-3 third hole.
Strange, who captained the United States Ryder Cup team in 2002, landed on the fringe with his second shot at the seventh. He chipped in for birdie, then sank a 15-foot birdie putt at the eighth to make the turn at 3-under-par 33.
At the 197-yard, par-3 11th, Strange hit a 6-iron to 6 feet. He rolled in that birdie putt and two holes later, knocked a pitching-wedge inside a foot for a tap-in birdie.
He parred his final five holes for his lowest round since joining the Champions Tour earlier this season.
'The last thing I want to do is get ahead of myself,' admitted Strange. 'You've got to be precise here. I got a little sloppy at the end. It's one baby step at a time.'
Strange has struggled a bit since his debut on the elder circuit. His best finish was last week with a 26th-place showing at the Liberty Mutual Legends of Golf, but Strange knows it won't all come at once.
'It's coming back slowly. I'm not going to fool myself,' said Strange. 'I'm still trying to get in golf shape. I'm real close now.
'What I've learned is that in a three-day event, there's no room for error. Tomorrow could be difficult for me. I hope not. I'm just trying to do my best each week.'
Johnson mixed two birdies and a bogey on his front nine, then birdied three of his first four holes on the back nine. He missed a 4-foot par save at the 14th, but reclaimed the lost stroke with a 14-foot birdie putt at the par-3 16th.
Johnson, a former beer delivery man, picked up his first Champions Tour victory earlier this year at the Toshiba Senior Classic.
'The win at Toshiba meant a lot less stress. It was a dream come true,' said Johnson. 'I've got lots of confidence now. I've had great support. Everybody has been awesome to me.'
Bryant was outstanding on the front nine with four birdies and no bogeys. He tallied a pair of birdies and a pair of bogeys on the second side for his share of second.
Dana Quigley, the winner of the season-opening MasterCard Championship, shot a 2-under-par 70 and is tied for seventh place with Leonard Thompson, Chuck Westergard, Morris Hatalsky, Walter Hall and Graham Marsh.
Defending champion Larry Nelson carded an opening-round, even-par 72.