The 63 also equaled the mark Fred Gibson set in last year's event and the first-round score of McCord on Friday. The 199 broke Larry Mowry's 1982 score of 201.
Nelson went at the 18th green in two, a move that most players avoided all week because of water guarding the green. His three-wood approach from 220 yards landed safely on the putting surface, but his eagle putt stopped on the lip. Nelson tapped in for the birdie and a one-shot lead over Gilder, and a two-shot edge over McCord.
Click Here for Larry Nelson's scorecard.
Gilder laid up at No. 18 but his second shot landed in the left rough and put him in a position where he could only get the ball 40 feet from the hole. Gilder's birdie putt that could have forced a playoff stopped five feet short of the hole and Nelson won for the fifth time on the Senior Tour in 2001.
'Pretty good day,' said Nelson, who earned $210,000 for the win. 'I knew I probably needed birdie on the last hole. I had laid up on Friday and Saturday. I felt the gamble on 18 was worth it.'
Nelson started a birdie tear at the second hole when he played a 7-iron to three feet. He added another at the third with a 15-footer. It was not until the sixth hole that Nelson really turned it on.
At No. 6, he converted a six-foot birdie putt and after a sand wedge into the seventh green left him with only a three-footer for birdie, he was already near the lead. Nelson drained a 35-foot birdie putt at No. 7 and made it four birdies in a row when he two-putted from 20 feet at the par-5 9th.
The 54-year-old once again had an eagle opportunity at a par-5 hole, this time it was the 512-yard 11th. He had only 15 feet for eagle, but missed the putt and walked off with the birdie. Nelson picked up his eighth birdie of the round at No. 13 when he made a 12-footer.
Nelson won for the fifth time in 2001 but for the first time since the Farmers Charity Classic in July.
'I think there were two or three goals for me this week,' said Nelson, who won for the 16th time on the elder circuit. 'One was to win since I hadn't won since July. Second was to not make any mistakes. To come back and play this well is gratifying.'
McCord, who was tied for the lead going into Sunday's final round, shot a 67, which included a chip-in birdie at No. 15.
Gilder racked up eight birdies and two bogeys on Sunday but failed to grab his second win of the season.
'I played well today,' said Gilder. 'I was just upset with myself on the last hole. I made a mental error. I should have gone for it in two. I just didn't know the golf course well enough.'
Defending champion Doug Tewell finished alone in fourth place at 13-under par.
Ray Floyd, Bobby Wadkins and Bruce Fleisher shared fifth at minus-10.
Click Here for Full-Field Scores from the SBC Championship