Stadler birdied the last to shoot 2-under 70. James, who played alongside Stadler, managed a 69. Meanwhile, Haas matched the low round of the day with his 7-under 65. The trio stands at 11-under-par 133.
Morris Hatalsky eagled the par-5 18th for his second straight 5-under 67. He is alone in fourth at minus-10. Dana Quigley tied Haas' 65 to move into a tie for fifth at 9-under-par 135. He stands alongside Andy Bean (69) and Brad Bryant (67).
Stadler, who has not won since the 2004 season, and James, who is winless since 2005, exchanged the lead early in the round. James birdied the first to join Stadler at minus-nine.
James moved out in front with a birdie on four. Stadler bogeyed the next to fall two back and James stretched his lead to three with a birdie on the par-5 sixth. He parred the final 12 holes to finish at minus-11.
Stadler erased his mistake from the fifth with a birdie on No. 7 at The Old Course at Broken Sound Club. However, he gave that stroke right back with a bogey on eight.
The 53-year-old got back to even-par for his round as he sank a 10-foot birdie putt on 10. Stadler tapped in a 2-footer for birdie on 13, but three-putted for bogey on 14 when it looked like he would pick up a shot on James.
James' tee shot to the par-3 14th found water left of the green. After a drop, he chipped in to save par then watched Stadler make bogey to fall two back.
Stadler atoned for that error with a 7-foot birdie putt on 15. He got up and down for birdie on the 18th to join James and Haas at 11 under.
Haas, who played two groups ahead of James and Stadler, opened with a birdie on the first. He flew up the leaderboard with three straight birdies from the third.
The reigning Senior PGA champion faltered to a bogey at nine, but came right back to birdie the 10th to get to 8 under. Haas birdied the 12th and 17th to move within one of the lead.
Haas knocked his second shot to seven feet at the par-5 18th, but settled for a two-putt birdie as he narrowly missed his eagle effort.
'Both days I've driven the ball really well and I think that's the key here,' Haas stated. 'The greens are fairly receptive too. If I can keep putting it in the fairway then I can attack the pins. Hopefully I can drive it well again (Sunday).'
R.W. Eaks posted his second straight 4-under 68 and is now alone in eighth at 8-under-par 136. Keith Fergus and John Jacobs are one stroke further back at minus-7.
Nick Price, who is making his Champions Tour debut this week, managed his second straight 71. He is tied for 35th at minus-2.