The home favourite entered day three with a one stroke advantage and while he was put under pressure during the round, the 33-year-old responded brilliantly to everything that was thrown at him.
He bookended a front nine of 32 with eagles and pulled away down the stretch to sign for a 64 and get to 21 under.
Sullivan claimed all three of his European Tour wins in 2015 and pushed Rory McIlroy all the way at the season ending DP World Tour Championship, Dubai as he claimed a place in the team for the 2016 Ryder Cup.
He achieved his best finish of the season earlier in the UK Swing by finishing fourth at the Betfred British Masters hosted by Lee Westwood, and will now take the lowest 54 hole score and largest third round lead of the 2020 Race to Dubai into Sunday.
"My strategy will be the same as today," he said. "Just control what I can do. I can't control anyone that is going to come up behind me.
"This golf course does offer a lot of birdies so I'm sure at some point someone is going to have a run at me. All I can do is control what I can do and see where we are at the end of it."
He added: "I was swinging it well and just trying to give myself as many chances as possible. As I was swinging it well a lot of shots came off today and I gave myself a lot of chances. It was good fun out there.
"I didn't realise I was five in front until I was coming up the last. I was just trying to make as many birdies as possible to be honest without forcing a mistake... like a three putt on 13. Just trying to control my situation and keep hitting the good golf shots that I have been hitting all week."
The par four first was playing just 278 yards and Sullivan's faded tee shot just cleared the sand and took a nice bounce to two feet to set up an eagle and a two shot lead.
I'm sure at some point someone is going to have a run at me. All I can do is control what I can do and see where we are at the end of it
He got up and down on the par five second but dropped a shot on the fourth and Stone moved past him with a front nine of 30.
The Rolex Series winner holed a long putt on the first, took advantage of the second, put tee shots to inside ten feet on the fourth and sixth, drove to the front of the seventh green and made the most of the ninth.
His lead was brief as Sullivan got a nice bounce with his second into the ninth and after he holed from three feet for an eagle, he had a lead he would not relinquish over the rest of the day.
A wonderful bump-and-run set up a birdie on the 12th and while he dropped a shot on the next after a three putt, he hit back in style.
He holed from 20 feet at the 14th to lead by four, restored that cushion with a tee shot to three feet on the 16th, and moved five ahead with an approach to five feet on the next.
Brown was unlucky as he hit the pin on the sixth with his ball looking destined for a hole-in-one, and sandwiched that with birdies on the par fives as he turned in 33.
Another gain on a par five came on the 12th and he added to that on the 15th and from 20 feet on the last, recovering from a bogey when he found the trees on the 17th.
Stone could not carry his momentum into the back nine as bogeys on the 14th and 16th saw him sign for a 67, a score matched by Otaegui, who recorded six birdies and two bogeys.
Burmester made an eagle and three birdies but also registered a bogey and a double in a roller coaster 69.
England's Laurie Canter, Belgian Nicolas Colsaerts, Australian Jason Scrivener and Dane Martin Simonsen were at 14 under, a shot clear of English trio Marcus Armitage, Dave Coupland and Jordan Smith, Welshman Jamie Donaldson, Kiwi Ryan Fox and South African Wilco Nienaber.