John Bland (67), Bruce Fleisher (70), J.C. Snead (70) and Bruce Summerhays (70) share third place at 5-under-par 139.
Levi bogeyed the par-4 seventh when he hit a poor iron shot into the bunker on the right side. He made up for it with a birdie at the eighth, then added another at the par-5 10th.
'Then I got my act together,' said Levi, after his bogey at seven. 'I had enough good chances.'
At the 11th, Levi holed a 16-foot birdie putt then parred the 12th. At 13, Levi sank a 25-footer for birdie and made it two in a row at the par-5 14th when he lagged a putt from the fringe to tap-in range.
Levi had looks at birdie on both 17 and 18 but missed and on both holes left himself with tough three-footers. He canned both of them and could be on his way to his second victory on the Champions Tour.
'The wind was blowing a lot different today than it was the last few days,' said Levi, who won last year's 3M Championship. 'I hit the ball fairly well and dropped a few putts.
'Tomorrow is the day. You have to get out there and produce. If you want to win golf tournaments, you have to go out and take them.'
Pooley, who won the 2002 U.S. Senior Open in a thrilling duel against Tom Watson, managed only one birdie on his front nine but birdied the 10th. He missed the green with his second at the par-5 hole but chipped to two feet and kicked in the short putt.
Pooley was in a bunker at the 11th and blasted his third 18 feet past the hole. He missed his par-saving putt right and dropped his first shot of the round.
He rebounded with a birdie at No. 12, then rattled off five pars in a row. At the par-5 closing hole, Pooley was short and left with his second shot. He pitched to six feet and drained the putt to join Levi in a share of first place.
Bland was flawless on Saturday with five birdies and no bogeys. Perhaps his finest shot of the round came with his third at the par-5 14th. He hit the flagstick in the air but the ball bounced 10 feet from the hole, where Bland could not convert the putt.
Fleisher, a two-time winner of this event, was even par through the first 14 holes. He birdied the 15th, then laid up at 18 and the decision paid off as Fleisher knocked his third to eight feet and holed the putt.
'Nobody seemed to move too much,' said Fleisher, who lives in nearby Ballen Isles. 'I thought the pins were very difficult. I'm looking forward to tomorrow. You better hit it solid.'
Snead held the lead in the middle of the second round after five birdies and two bogeys through his first 12 holes. At 13, he landed in a bunker, blasted out to 15 feet and missed the par putt.
Snead also dropped a shot at the 17th when he met another sand trap, but birdied 18 to get within one shot of the lead. He will be in search of his first victory since the 2002 Greater Baltimore Classic and that was seven years from his last win.
Summerhays shared first with Levi, but fell apart on 18. His fourth from the back bunker rolled 18 feet from the hole and his par-saving putt died right. Summerhays tapped in for his first bogey of the round.
Dave Stockton (68), Ed Fiori (69) and Morris Hatalsky (69) share seventh place at 4-under-par 140.
Overnight leader Tom Kite struggled on Saturday. He posted a 1-over 73, which included a double-bogey-7 at the closing hole. At that hole, Kite got his drive stuck in a palm tree.
Kite is tied for 10th place with Dick Mast (68), John Harris (67), John Jacobs (69) and Vicente Fernandez (69). That group is knotted at 3-under-par 141.