Levi's two-day total of 3-under-par 137 marks the highest score to hold the lead through the midway point of the championship since 1990 when Harold Henning and Gary Player shared the top spot.
The four players at the top are the only golfers under par at Firestone Country Club as high rough and slick greens have made play difficult.
One of the best golfers on the over-50 circuit struggled Friday as Tom Kite, one of the three co-leaders after the first round, shot a 3-over 73. He is tied for 10th at 1-over-par and is joined by a large group headlined by former champions Hale Irwin and Ray Floyd.
Jack Nicklaus, who has battled back injuries, opened with a 1-over 71 Thursday but did not play as well in round two. He shot an 8-over-par 78 and made the cut on the number at 9-over-par 149.
Had Nicklaus not carded an even-par 35 on his second nine Friday he could have missed the cut and in the process snapped one of the most impressive streaks in his storied career. Nicklaus has made every cut in a major tournament since joining the elder circuit in 1990, a streak that has now reached 46 consecutive championships.
'I don't worry about cuts - I'm more interested in hitting good shots,' said Nicklaus, who has been forced to withdraw from two majors on the Senior Tour. 'I was pretty pleased with the back nine. You know, I don't really worry about my injuries, it's just years of playing golf taking its toll. All I can do is take one shot at a time. Some days you are good and some days you aren't, and today I wasn't very good.'
Jim Thorpe, the first major champion of the year at The Tradition, is tied for fifth place with Jay Overton, Bobby Wadkins, Bob Gilder and Fuzzy Zoeller. The group stands at even-par 140.
Levi has only one top-five finish this season in 10 starts, a tie for fourth at the Farmer's Charity Classic two weeks ago. Levi won 12 times on the PGA Tour, including four wins in 1990 en route to being named PGA Tour Player of the Year.
Levi's brief career on the Senior Tour has been filled with ups and downs with the short stick. He took 32 putts in Thursday's round of 69 but only needed 24 to get around Firestone in the second round.
'The putting has been fairly poor, so that's what probably has kept me from doing better than I have,' said Levi, who ranks 62nd in putts per round on tour with an average of almost 30 putts a round. 'This poor putting has killed me, but I'm out here to win tournaments.'
Friday's second round was highlighted with more ups and downs for Levi. Levi shot an 1-under-par 34 on the front side with three birdies and a pair of bogeys.
At the turn, Levi was tied for the lead at 2-under-par but he broke out of the pack and drained the birdie putt to go to 3-under. Levi extended his lead two holes later when he played a 5-iron to 20 feet, where he cashed in on another birdie putt.
Levi did not take long to squander his edge. At the 15th, Levi blocked his tee ball into a right greenside bunker where he left his bunker shot on the fringe. He chipped to four feet and rolled home the bogey putt but still maintained a one-stroke lead.
Levi, who turned 50 in February, looked in great shape at the par-5 16th when he ripped one down the center of the fairway before he pushed his second shot in the right rough under a tree. Levi's third bounded off the green and his chip on to the green left him six feet from the hole, where he missed to fall back into a tie for first at minus 2.
He rebounded at 17 when once again he striped his drive down the fairway and played a 6-iron five feet behind the hole. Levi holed the birdie putt to take the 36-hole lead at 3-under-par.
'Early on I played a couple of bad shots but after that I started to settle down a little bit more and started hitting the ball quite well,' said Levi. 'There's a lot of tough holes out there. You have to keep at it.'
Nelson, Ziegler and Hall each posted rounds of 2-under-par 70 Friday and each player loved the level of difficulty that Firestone offers.
'(Firestone) feels more like the U.S. Senior Open than our Opens have been,' said Nelson, considered the best Senior player never to win a major on this tour. 'We haven't played a U.S. Senior Open course that's been as difficult. I think it's great. There's no reason to make our majors a pitch-and-putt.'
'I think this is the hardest, fairest course I've ever played. No gimmicks,' Ziegler said. 'Guys love coming here to play golf. We play so many courses where you feel like you're playing Mickey Mouse. They've got big, old rolly greens. It's not fun to play what they're building today.'
'Today is a great example of a perfect weather day to play, yet the scores are not low,' said Hall, a former salesmen. 'The course will not allow it.'
Tom Watson, the 2001 champion, struggled to a 6-over 76 Friday and shares 36th place at 5-over-par.
The 36-hole cut fell at 9-over-par 149 and 80 players advanced to the weekend.
Full-field scores from the Senior PGA Championship