Bruce Fleisher carded a 2-under 70 to finish one shot off the pace at 5-under-par 139. Dana Quigley held the lead down the stretch but a double bogey at the par-4 17th dropped him back into a tie for fourth with Mark James and Brad Bryant at 4-under-par 210.
Levi began the day in a tie for 13th and picked up his first birdie at the par-5 second on the Hills Course at The Hills Country Club. Levi then played his tee shot to 12 feet for a birdie at the par-3 third but he gave that shot back with a bogey at the very next hole.
The 53-year-old recovered with a birdie at the par-5 eighth but he stumbled to a bogey at the par-5 10th. Levi countered at the par-3 11th and hit his tee shot inside 4 feet for another birdie.
Levi parred his next five holes until he hit a 6-iron from 182 yards out into the bottom of the cup for an eagle at the par-4 17th. Levi closed out his round with a birdie at the last to grab a share of first with one round to play.
'I always like to be up near the lead but tomorrow's a new day,' said Levi, who will be in search of his third Champions Tour victory on Sunday. 'I think lots of pars and sprinkle in some birdies will be good enough.'
Thorpe dropped an 8-iron inside 6 feet for a birdie at the par-4 first and drained an 8-foot putt for a birdie at the third. He continued his fine play on the front nine with a birdie at the par-4 ninth after his second shot stopped within 4 feet of the hole.
He found trouble with a bogey at the 11th, however, and dropped another shot with a bogey at the 16th. Thorpe then hit a tremendous second shot to the par-4 17th that rolled within inches of the cup for a tap-in birdie.
Thorpe elected to hit a driver from the fairway at the par-5 closing hole but he topped his shot, sending his ball rolling towards the putting surface. He then hit a wedge to 35 feet and ran home the birdie try to join Levi in the lead.
'I'm hitting the ball very well, but I'm not putting well,' said Thorpe, who is seeking his 10th career victory on the senior circuit. 'If I can make a few more putts I'll be happy.'
First-round leader Curtis Strange managed a 74 on Saturday to join Mark Johnson in a tie for seventh place at 3-under-par 141. Morris Hatalsky and Hajime Meshiai followed at 2-under-par 142.
Defending champion Larry Nelson hung around with a 71 to share 11th place with Gil Morgan, Joe Inman and David Eger at 1-under-par 141.