Stadler, son of former Masters champion Craig Stadler, and Percy, who is appearing in only the ninth tour event of his career, turned in rounds of 5-under 67.
Anthony Kim was tied for the lead going to the final hole at the Redstone Golf Club, but his tee shot at the 18th found the water and he settled for a 68 that gave him a share of third place with Kevin Sutherland, James Driscoll and Vaughn Taylor.
Phil Mickelson and Padraig Harrington were part of a group of nine players at 3-under 69.
Blustery winds blew throughout the day on a course that is set up in a similar manner to the Augusta National Golf Club, where the world's top players will gather next week for the Masters.
Ernie Els, the only two-time winner on the circuit this season, shot a 70. Defending champion Paul Casey withdrew prior to starting his round because of a shoulder injury. Three-time Houston champion Vijay Singh withdrew with an injury after playing nine holes.
Fred Couples, who has won three of the first four events on the Champions Tour, fired a 71.
Swim Week Miami Beach 2014 [PHOTOS]