Mark James is alone in second place at 8-under 64 and Andy Bean is two strokes back at 66. Bobby Wadkins, John Harris, Morris Hatalsky and Tom Kite, a two-time runner-up this season, share fourth at 5-under 67.
Stadler started on the 10th tee on The Old Course at Broken Sound Club. He got off to a quick start with birdies on each of his first two holes. He cruised to five straight pars before a birdie on 17 moved him to minus-3.
The eight-time winner on the Champions Tour eagled the par-5 18th. Around the turn, Stadler birdied the first to take the lead at minus-6. He came right back with a birdie on two.
After three pars, Stadler rolled in a birdie putt on the sixth. Stadler made it two in a row as he birdied the seventh, then closed with back-to-back pars to cap a bogey-free round.
James also started on the back nine. He collected his first birdie on No. 11 and also birdied the 13th and 18th to turn in minus-3.
The Englishman climbed the leaderboard with a solid front nine. He birdied the first and came back with a birdie on No. 4.
Back-to-back birdies from the sixth moved James to 7 under. He closed with a birdie at the ninth, his last, to end one behind Stadler.
Jay Haas and Loren Roberts, who battled for Player of the Year honors in 2006, each opened with rounds of 4-under 68. They were joined in eighth place by Brad Bryant, Jose Maria Canizares, R.W. Eaks, Dave Eichelberger, John Jacobs, Tom Jenkins and Wayne Levi.
Among those at minus-3 are Allen Doyle, the two-time defending champion at the U.S. Senior Open.
Nick Price, making his Champions Tour debut, opened with a 1-under 71 and is tied for 33rd. He bogeyed three of his last five holes as he sprinkled five birdies and four bogeys through his round.