The 32-year-old finished with a pair of birdies at the Country Club of Jackson on Saturday for a seven-under 65 to reach 20-under and lead from Beau Hossler (68) with fellow American Kevin Yu (66) a further shot back.
Mitchell missed out on the FedEx Cup playoffs and is playing the fall events to see if he can finish in the top 60 to get into the first two $US20 million signature events of 2025 at Pebble Beach and Riviera.
A victory would get him in The Sentry at Kapalua, another $US20 million purse, along with the Masters.
"Only won once and trying to close the door a second time, which has been clearly very difficult for me," said Mitchell, whose lone victory was the Honda Classic in 2019.
Eight players were within five shots of Mitchell, with Bud Cauley (67), Lucas Glover  (68) and Jacob Bridgeman (69) tied fourth at 16 under and New Zealand's Ryan Fox (68) and Michael Thorbjornsen (69) a further shot adrift.
Of the leading six players, only Mitchell and Glover have won on the PGA Tour, though Fox has enjoyed success on the European tour.
Glover won in consecutive weeks last August but doesn't put a lot of stock into experience winning on tour.
"Everybody out here is so good and so seasoned to win," Glover said. "All the young guys coming up, it's like the program is different than 20 years ago. But coming down the stretch tomorrow nerves are nerves, and knowing how to handle it is difference.
"The depth of talent is so deep that there will be a lot of guys who probably aren't worried about nerves."
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