Williams earned his first win on the Sunshine Tour at this event in 1985. This time he held off a strong challenge from South Africa's Hennie Otto for the victory.
'The tension was unbelievable,' said Williams. 'There was no stage on the back nine where I felt comfortable. I was counting down every hole, and just telling myself to keep doing what I was doing.'
The duo was knotted at 15-under until Williams hit his approach to within three feet on the par-4 17th. He rolled in the birdie putt to pull away from Otto and secured the win with a 30-foot birdie putt on the 18th.
'It was exhausting out there,' said Williams. 'I was nervous the whole day. But I got off to a good start. I thought if I could get through those difficult first four holes then I'd be okay. I was 2-under through five holes, and that helped a lot.'
Williams began the day with a three-stroke lead over Otto, Titch Moore, Douglas McCabe and Tim Clark. He brought a stretch of 46 holes without dropping a shot into the final round.
The 42-year-old continued the streak with three birdies on the front nine to make the turn at 16-under. At the 12th, he three-putted for his first bogey since the first round while Otto made birdie to close the gap.
'The 12th was the one bad putting stroke I made all week,' said Williams. 'I left the first putt short, but the second was not that difficult. It was inside right and I pushed it.'
Williams held on until making back-to-back birdies from the 17th for his first win on the Sunshine Tour since the 1996 Leopard Rock Classic.
The 1998 Asian Tour Player of the Year lost his card on the Sunshine Tour last season. With the win, the veteran will be exempt for the next five years.
Martin Du Toir of South Africa fired a 7-under 65 to join American Bruce Vaughan (67) in a tie for third at 14-under 274.
Clark, the current money leader, was scheduled to make his return to the PGA Tour at the Pebble Beach Pro-Am this weekend, but decided to remain on the Sunshine Tour until the end of the season.
After capturing the co-sanctioned South African Open at the Durban Country Club two weeks ago, he position himself to finish atop the Sunshine Tour money list. A money title would earn him automatic entry into the World Golf Championship's World Match Play and the British Open.
The Durban native will play at next week's Dimension Data Pro-Am at the Centurion Lake Country Club as well as the Nashua Masters and the Tour Championship.
Full-field scores from the Telkom PGA Championship