"One of these times, it's going to come out in my favour, " Stricker said.
Johnson's nearest challenger is Stricker despite the veteran struggling with pain in his lower back.
England's Ian Poulter, the 2010 Match Play winner, set up a clash with 2001 champion Steve Stricker.
Poulter thrashed South Africa's Tim Clark 5 and 3 while veteran American Stricker beat Donald's conqueror Scott Piercy.
Four shots off the lead are a trio of Americans -- Ryan Palmer, Steve Stricker and Cameron Tringale.
In the morning wave of play on Friday, veteran Steve Stricker had the best round, a two-under 68.
But the 37-year-old then bogeyed three times, while Steve Stricker's chances went when he finished with back-to-back bogeys.
Also capable of winning are the savvy old-timers Steve Stricker and Jim Furyk.
Stricker, one of the game's best putters, told Woods to keep his hands more in line with the ball.
WSJ: Tiger Woods Should Credit His Return to No. 1 on Improved Putt
Stricker is one stroke ahead of Vaughan Taylor after shooting a fine third-round 61 to remain in pursuit of Perez.
Stricker, who was at 14-under 199 to tie the 54-hole record at Westchester, has not won on tour since 2001.
Baddeley finished with a five-under 66 to finish runner-up on 20-under 264, with Stricker two strokes further adrift on 266.
Players might be lining up to force Steve Stricker into full retirement for the putting tip he gave Woods at Doral.
Meanwhile, world No. 1 Luke Donald completes an under-the-radar march (69-69-69) to tie Woods and Stricker at four off the pace.
WSJ: The Masters: Tiger Woods, Rory McIlroy Should Be in Contention on Sunday
He sank five birdies on his inward nine holes for a five-under effort to lead US compatriot Steve Stricker by two.
Elsewhere in the foursomes, Tiger Woods and partner Steve Stricker beat Australian Geoff Ogilvy and Japan's Ryo Ishikawa six and four.
American world number six Steve Stricker was on his own at six under after a 68 with countryman Heath Slocum five under.
Defending champion Steve Stricker lounged on a sofa in the dining room watching the NFL playoffs with Dustin Johnson and Brandt Snedeker.
Six players, including defending champion Steve Stricker, had not even teed off.
Compatriot Stricker, 41, eight shots behind Perez at the start of his third round, is searching for his first Tour win since 2007.
Steve Stricker missed out on becoming only the fifth player to win a PGA Tour tournament four successive times, finishing tied for fifth.
David Albright and Andrea Stricker, of the Institute for Science and International Security, said the latest test could be a measure of progress.
One stroke behind Woods and Briton Rose is a quartet of Americans -- Bo van Pelt, Steve Stricker, Matt Kuchar and Scott Piercy.
American Phil Mickelson, who has chosen to rest this week, leads the standings ahead of Barclays Classic champion Steve Stricker, with Woods in third.
He has slid from second in the world ranking to third behind Steve Stricker after just one top-10 finish in seven starts this season.
Steve Stricker, plodded his way around Augusta more methodically to end up in the same place as Johnson after two rounds is, stands one- under-par.
WSJ: At the Masters, the Eighth-Grader Gets Detention | Golf Journal by John Paul Newport
Stricker and Woods are second and third respectively on the new FedEx Cup points list, behind leader Phil Mickelson, who has taken the week off.
Ian Poulter and Ross Fisher are tied with Tiger Woods and Steve Stricker, while Lee Westwood and Martin Kaymer lead Phil Mickelson and Dustin Johnson.
"Everybody knows their strengths and I know mine, " Stricker said afterwards.
WSJ: At the Masters, the Eighth-Grader Gets Detention | Golf Journal by John Paul Newport
America's Jim Furyk, Ricky Fowler and Steve Stricker are currently tied for ninth at two-under par alongside England's Lee Westwood and two-time champion, Germany's Bernhard Langer.
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