Verplank, as a teenager growing up in Dallas, got to play several rounds with Nelson.
After holing a final 2-foot par putt at No. 18 for a one-stroke victory, Verplank dropped into a squat and looked skyward with smile on his face. He pumped his left fist triumphantly into the air.
"Byron meant to much to me," Verplank said. "To be from Dallas and win this is unbelievable."
Sadly missing for Verplank was a personal congratulation from Nelson, who died last September at age 94. But Nelson's wife, Peggy, was there clutching one of his famed fedoras in her hand when she hugged Verplank.
"Byron would be very, very happy for Scott. I am, too," Peggy Nelson said. "The friendship they had, it's great to see it culminate this way."
In 1968, Nelson became the first golfer to have a U.S. PGA Tour event named after him, and he would always greet players finishing their rounds at the 18th green before taking part in the trophy presentation.
Verplank closed with a 4-under-66 for a 13-under 267 total, a stroke ahead of Donald (68) for his fifth U.S. PGA Tour victory, his first since the 2001 Canadian Open. Phil Mickelson (65), Jerry Kelly (64), Rory Sabbatini (64) and Ian Poulter (66) tied for third at 10 under.
Clinging to a one-stroke lead, Verplank hit his tee shot at the 196-yard 17th hole into a bunker far away on the side opposite the hole. But he saved par - and the long-desired championship - after blasting to less than 2 feet.
Verplank and Donald both had pars at No. 18 after both slid similar 10-foot birdie attempts past the hole.
This victory was much more valuable to Verplank than the $1.134 million (830,000 EUR) check and a custom-made motorcycle built by Orange County Choppers.
It was the 21st Nelson tournament for the 42-year-old Verplank, who considers the event his fifth major because of the man for which it's named - and the legendary golfer who used to write him encouraging notes. Verplank once was a standard bearer at the tournament, where his mother was a volunteer.
After Saturday's round of 66 got him within one stroke of Donald for the lead, Verplank said winning would be the highlight of his career.
Donald led by three strokes after his 12-foot putt at the 438-yard sixth hole for his third birdie in a four-hole stretch on Sunday. But that was the same hole that Verplank began his birdie run with a 5-footer.
Verplank was within a stroke at 12 under after chipping to 2 feet for birdie at the 533-yard seventh hole and making a 12-footer at No. 8.
Things went wrong for Donald at the ninth hole.
Donald's drive at the 439-yard hole went into the trees on the left, and his approach shot from there wound up in the rough to the eight of the green. The Englishman hit his next shot over the green and left his chip 12 feet short before his bogey putt skidded past the hole.
Even though Verplank's 8-foot birdie attempt slid past the hole, he was in the lead.
Verplank made a 13-foot birdie putt at No. 11, curled a 16-foot birdie attempt just over the top of the hole at Ho. 12 and then made a 23-foot putt at the 183-yard 13th to get to 14 under - four strokes ahead of Donald.
Verplank missed the fairway and had bogey at No. 15, then had to settle for par after finding a greenside bunker at the 554-yard 16th - the easiest hole on the course. Donald blasted out of a bunker to 4 feet for his birdie that got him back within a stroke.
The closest Verplank had come to winning the Nelson before was in 2001 when he lost a four-hole playoff with Robert Damron. That was the first of three top-10 finishes the last six tournaments, though shoulder problems forced him to withdraw from last year's tournament - the final one attended by Nelson.
Mickelson, in his first tournament since the Masters and with Butch Harmon as his instructor, had two chip-in birdies on the first seven holes.
Mickelson came up only inches short of another chip in at No. 8, then hit his approach to 3 feet at No. 9 for a birdie to get to 9 under. But he couldn't keep up his charge on the back nine.