Two years ago, he made the turn in the final round of the Greenbrier Classic with a one-stroke lead before finishing two strokes out of a playoff won by Scott Stallings. Last year Simpson lost a one-shot lead on the back nine again with three straight bogeys and tied for seventh.
Simpson, Brendon de Jonge and Jimmy Walker are the only players to have two top 10 finishes at The Greenbrier.
"(You) can't really afford a bad nine holes when you win," Simpson said. "I think it's just me continuing to keep playing well, and hopefully I'm in that position on Sunday where I do have a chance to win."
The last two Greenbrier Classics have gone to playoffs, and Stuart Appleby needed a birdie on the final hole for a 59 to beat Jeff Overton by a stroke in the inaugural tournament in 2010.
Mickelson is coming off top five finishes in three of his last four tournaments. But he has yet to shoot an under-par round at The Greenbrier, missing the cut each of the past two years.
Last year marked the first time that Mickelson and Tiger Woods missed the cut in a tournament as professionals.
Woods isn't entered this year. He has a sore left elbow and isn't playing again until the British Open.
Among others in the field are Jordan Spieth, the 19-year-old Texan in search of an elusive win that would give him his PGA Tour membership and make him eligible for the FedEx Cup playoffs. He finished sixth at the AT&T National. He's won more than $1.1 million this year and is assured of a tour card when the new season starts in October.