Nielsen, who didn't win in his five years on the PGA TOUR or in his five seasons on the Champions Tour, had a 12-under 130 total after 36 holes on the 7,011-yard Red Course at Eisenhower Park.
The three-shot lead matches the tournament record set by Bruce Fleisher in 1999 and 2000, and matched by Jay Sigel in 2001.
Sigel, who at 63 years, 7 months would become the tour's oldest winner, and defending champion John Harris were tied for third at 134.
Nielsen started the day in third place, two strokes behind Loren Roberts and one behind Eduardo Romero. His round didn't get off to a great start as he bogeyed the par-3 2nd, but he birdied the next hole, a par-5, and added two more on the front side, including a 40-foot putt on the par-4 6th.
He began his back-nine birdie binges with a 15-foot putt at No. 11 and added others on 12, 14, 15 an 17, the last a two-putt from the fringe on the par-5 17th.
Nielsen, who turned 54 on Friday, had a successful amateur career and won 32 titles in lower level PGA events, including the New York State Open in 1985 and 1989.
McKnight, a longtime amateur who turned professional for the second time in 2001, had a bogey-free 66. Like Nielsen, he has one top 10 finish this season.
Sigel, one of the most successful amateurs ever, has been battling various injuries the last few years, and his 66 left him a position for a third straight top 10 finish.
Harris, who beat Tom Jenkins in a one-hole playoff here last year for his first Champions win, had a 67.
Roberts, who opened with a 64, had a second-round 71 and was tied at 135 with R.W. Eaks (66), David Edwards (67), Bob Gilder (67) and Brad Bryant (68). Romero also had a par round of 71 Saturday and was at 136 with Bruce Summerhays (65) and Curtis Strange (68).
Jay Haas, the winner of the tour's last tournaments and a four-time winner this year, had a 72 and was at 139.
The winner gets $225,000 from the total purse of $1.5 million. ... Fleisher won both times he had a three-stroke lead entering the final round and Sigel finished in a tie for fourth. ... Nielsen was two strokes of the best 36-hole score in tournament history, a 128 by Jim Thorpe in 2003. ... Mike Fetchick won the Hilton Head Seniors Invitational in 1985 on his 63rd birthday, the oldest tournament champion.