Tom Purtzer, David Peoples, Brad Bryant and David Eger opened with 68s at Fallen Oak. Mark O'Meara, coming off his first Champions Tour victory last week with Nick Price in the Legends of Golf team event, was two strokes back at 69 along with Eduardo Romero and Ted Schultz. Price had a 70.
Thompson, who won the last of his three Champions Tour titles in 2001, has cut his tournament schedule but has been playing almost every day at home in Ponte Vedra Beach, Fla., at Sawgrass Country Club and TPC Sawgrass.
"I think it had something to do with it. Yes, I do," Thompson said. "I really do. ... You can't find too many places that you go from one to the other that are as difficult as those two on a daily basis. That's where we've been playing. I'm not saying that that was the be-all end-all, but it certainly helps."
The 51-year-old Tway birdied Nos. 12, 14 and 16 to match Thompson at 5-under.
Tway said staying out of trouble areas was the key to his score.
"I'm pleased with how I played," Tway said. "The golf course, I think everybody likes it. It's in wonderful shape. If you can avoid the bunkers, that's the starting point, I think, off the tee because they're awfully penal. ... It was a challenging day because of the wind, but I was pleased with how everything went."
Thompson bogeyed the second hole but then ran off four straight birdies. He also bogeyed No. 11 and then birdied Nos. 13-15 before closing with three pars.
Bernhard Langer, a two-time winner this year, opened with a 72.
Jodie Mudd and Bobby Clampett made their Champions Tour debut. Clampett had a 72, and Mudd shot a 74.