Pate, winner of the 1976 U.S. Open, fired a 4-under 68 that gave him a two-day total of 6-under 138 at the Laurel Valley Golf Club.
Arnold Palmer, who grew up on this course, shot an 86 in what was likely his last competitive round in his home area. But he made a 20-foot birdie putt on the 17th hole and narrowly missed a 40-footer at the 18th.
"The local people have, for all my life, been extremely supportive of me and my golf," Palmer said.
Pate's most recent victory came at the 1982 Players Championship. He has nine top-10 finishes in his Champions Tour career.
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