The last player to win a tournament without carding a bogey was Jesper Parnevik in 1995.
He and Wilson lead by two shots from Americans Fred Couples and Billy Mayfair, and Swede Jesper Parnevik.
Bernhard Langer is four shots off the lead while Jesper Parnevik is one shot further back after a 69.
Parnevik, who had hip surgery at the end of September, said Friday's 65 was his best round since going under the knife.
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And in 1997, Leonard made up five shots on Jesper Parnevik on Sunday to make it five straight American winners at Royal Troon.
Former British Open champion Paul Lawrie of Scotland and Paul Gow of Australia followed at 8 under, while Sweden's Parnevik finished at 7 under.
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Also among those who failed to qualify were South Africa's Trevor Immelman, Swede Jesper Parnevik, Australians Aaron Baddeley and Peter Lonard and 1986 USPGA champion Bob Tway.
Players like Phil Price, Paul McGinley, Thomas Bjorn, and Monty are struggling to get anything going, and Jesper Parnevik and Lee Westwood are shockingly out of form.
The rumours about his personal life have made front-page news across the world and fellow pro Jesper Parnevik, who introduced Woods to his wife Ellin, has led the criticism.
These players need to get back to basics before the big event and although I disagree with not using players until the last day, Parnevik and Westwood may give Torrance no choice.
American Paul Goydos stood alone in third on eight under after matching Axley's round-of-the-day 63, while Swede Jesper Parnevik survived the cut by one shot after a disappointing round of 71 left him on even par.
Usually around half of the 140-strong field at a tournament will be cut at the halfway stage, but Parnevik's 18th-hole miss meant that the weekend ranks were swelled to a number not seen since the 1981 Travelers Championship.
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