Canadian John Irwin posted a 3-over 74 to finish in second place at even-par 213. South Africa's John Bland followed at 1-over-par 214 while John Chillas of Scotland and five-time British Open winner Tom Watson were at 2-over-par 215.
Strong winds plagued Royal County Down as only one player shot even-par. Sugai started with a three-stroke lead and seemed undeterred by the gusts with two birdies over his first four holes to move to 10-under.
As his competitors faltered, Sugai dodged the wind and had a six-shot lead through seven holes. However, the Japanese player could not escape the conditions for long. Sugai ran into trouble with back-to-back double bogeys starting at the eighth to make the turn at minus-6.
Sugai's lead stood at three but he added to his advantage with a birdie at the 12th. He recorded another birdie at the 16th to return to 8-under before closing with back-to-back bogeys from the 17th.
The 52-year-old's challengers also found trouble coming in. Bland bogeyed his final two holes while Chillas closed with a pair of double-bogeys.
Sugai, who has won four times on the Japan Golf Tour and three times on the Japan Seniors Tour, is looking to make a name for himself outside his home country.
With a six-shot edge heading into Sunday's final round, Sugai can become the first wire-to-wire winner of the Senior British Open since Gary Player accomplished the feat in 1988.
'I still can't believe what's happening,' said Sugai. 'I felt a lot of pressure when I had those two double-bogeys but now I want the wind to blow, blow, blow because I hit the ball nice and low.'
Watson was five shots off the pace to start the round but the 52-year-old got off to a dismal start with four bogeys over his first six holes. Watson made a brief recovery on the back side with three birdies but a bogey and a double-bogey squashed his efforts.
'The course won, I'm afraid,' said Watson, who is making his debut in the tournament. 'It's as simple as that. I didn't put up much of a challenge. Now it's up to Mr. Sugai. It's his tournament to win or lose.'
Christy O'Connor, Jr., who won this event in 1999 and 2000, posted a round of 2-over 73 to finish at 3-over-par 216. Japan's Katzunari Takahashi was one shot further back at 4-over-par 217 after a round of 77.
David Oakley and Nick Job share eighth place at 5-over-par 218. They were followed by John Morgan and Russell Weir, who are knotted at 6-over-par 219.
John McTear of Scotland, the only player to shoot par, finished at 7-over-par 220 for the tournament. McTear had five birdies on his round to go along with five bogeys for a 71.
'It was very tough out there,' said McTear, who could have shot below par if not for bogeys on the last two holes. 'Normally, I hit my shots low so that helps.'
McTear was joined by David Huish, Priscillo Diniz, Mike Miller, Ross Metherell, Seiji Ebihara and Malcolm Gregson in a tie for 12th.
Full-field scores from the Senior British Open