R.W. Eaks, Mark Johnson and Delroy Cambridge finished one shot off the lead at 15-under-par 273. Mike San Filippo and Harry Taylor are tied for fifth at 14-under-par 274 at The King & The Bear.
Meshiai held a two-stroke lead to start the day and was cruising along early with a birdie at the par-4 second and an eagle at the par-5 fifth. He found trouble with a bogey at the par-4 eighth to make the turn at 15 under.
The 50-year-old from Japan, whose best finish on the Champions Tour this season was a tie for ninth at the FedEx Kinko's Classic, tallied a birdie at the par-5 13th but gave that shot back with a bogey at the very next hole.
Meshiai recovered with a birdie at the 16th but stumbled to another bogey at the 17th. Meshiai countered with a birdie at the last to secure the outright lead.
Eaks had a hot start with three birdies and an eagle over his first six holes. He added a birdie at the 10th but faltered to a double bogey at the par-3 11th. Eaks then birdied the 18th for a round of 67.
Cambridge mixed eight birdies and four bogeys for a round of 68 while Johnson fired a 66 for his share of second.
Dick Mast, Don Reese and Mike Malaska share seventh place at 13-under-par 275.
The 72-hole cut fell at 3-over-par 291 with 72 players surviving for the final two rounds.