Wadkins shot a 5-under 67 for the second straight day to get to 10 under.
Wadkins, who won his first career major this season at the Senior Players Championship, shared the lead after the first round with Wayne Levi and defending champion Loren Roberts.
'I've been trying to play for the middle of greens and make pars and I've been doing a good job of that,' Wadkins said.
He did a better job on the final holes, carding birdies on three par-5 holes, Nos. 15, 16 and 18 -- nearly knocking in his shot from the bunker for eagle on 15.
Levi faded, shooting 75. Roberts shot 71 to finish in a five-way tie for third.
Roberts entered The Tradition with four wins this season and the lead in Charles Schwab Cup points race. He was supposed to be paired with Peter Jacobsen, but played alone after the Oregon native withdrew with hip pain.
Tom Jenkins shot a 68 to move to 6-under with Roberts, Tom Purtzer, Keith Fergus and last week's winner, Tom Kite.
Wadkins, who never won on the PGA Tour but has two Champions Tour wins this season, has shot four straight rounds of 67 or better. Last week at the Boeing Seattle Classic he shot 64 and 65 in his last two rounds en route to a ninth-place finish.
Jacobsen, whose event management company runs the Tradition, has suffered from hip and knee problems for the past few years and may have to have hip replacement surgery.
'It's getting worse,' the 52-year-old said. 'It's getting to where its affecting my temper on the course. I'm beginning to think I can't win because I'm concerned on the course about how my hip feels. It's kind of affecting my overall outlook and that's not good.'
Jay Haas, second to Roberts in season points, was 1-over after rounds of 73 and 72.
The Tradition was played for 14 years in Arizona before Jacobsen lobbied to relocate it in 2003. Jacobsen's sports management firm runs the tournament, which is sponsored by Jeld-Wen, an Oregon-based window-and-door maker.
Next year, the tournament is moving to Crosswater Golf Club in Sunriver, an up-and-coming central Oregon resort town, where it's hoped it will attract bigger crowds.