Jim Dent fired a 7-under 65 to finish one shot off the lead along with Des Smyth at 6-under-par 138. Ed Fiori was one shot further back at 5-under-par 139.
Sigel, who won this year's Bayer Advantage Celebrity Pro-Am, began the day in a three-way tie for first with Nelson and Smyth but he managed to jump out of the gate with back-to-back birdies from the first.
He stumbled with a bogey at the fourth but ran off back-to-back birdies again starting at the par-4 sixth to move to eight-under.
Sigel found trouble with a bogey at the par-3 eighth and coasted at even par before dropping another shot with a three-putt bogey at the par-3 14th.
The 59-year-old recovered and tallied a four-foot birdie at the par-5 16th for his share of first as rain continued to plague Hayfields Country Club.
'The golf course did not play easy today,' said Sigel. 'Hard to get some rhythm.'
While Sigel is looking for his second Champions Tour victory of the season, Nelson is trying to return to the winner's circle for the first time since 2001.
Nelson started off well with a 15-foot birdie at the first and added a birdie at the fourth after his 7-iron stopped three feet from the cup.
The 56-year-old struggled to a bogey at the par-4 17th but responded at the very next hole with a birdie to join Sigel in the lead.
'Really hard day to get the ball close to the hole because of the conditions,' said Nelson. 'Just a day to survive.'
Dent had a remarkable round and nearly shot his age. The 64-year-old collected three birdies on the front nine and added four on the back to finish one shot off the lead.
'It's really important for me to play fast,' said Dent. 'I've been working a lot on my chipping and putting. It's important to be able to putt well out here.'
Should Dent come back to win on Sunday he would become the oldest winner in the history of the Champions Tour. Defending champion J.C. Snead became the third oldest player to ever win on the Champions Tour with his victory at this event last year.
Doug Tewell, John Bland and Tim Jenkins finished in a tie for sixth at 4-under-par 140.
Bruce Fleisher, Andy Bean, Isao Aoki and Tom Purtzer were one shot further back at 3-under-par 141.
Sam Torrance, who is making his debut on the Champions Tour, rebounded with a 4-under 68 to finish in a group at 2-under-par 142.