The Englishman fired a superb six-under 66 on the final day to close on 17 under par at the Royal Johannesburg and Kensington Golf Club, finishing clear of compatriots David Howell and Anthony Wall, Kevin Phelan, Jaco van Zyl and overnight leader Wallie Coetsee.
Sullivan laid the foundations for victory with a sparkling front nine, racing to the turn in just 32 blows with five birdies in eight holes before making his only mistake of the day at the 11th.
But he steadied himself with three solid pars and dropped his sixth birdie putt of the round at the 15th which gave him the lead when Howell pulled his tee shot into water a hole behind.
Wall???s challenge hit the buffers when he bogeyed 15 after finding water, and Sullivan held his nerve down the stretch and increased his lead further with a well-crafted birdie at the final hole.
The 28-year-old retreated to the clubhouse to watch the remaining groups finish up, and neither Wall or Howell were able to find the two birdies they needed over the last three holes to force a play-off.
The consolation for the English pair was that they also clinched the two other Open places on offer by virtue of their higher world ranking over their fellow runners-up.
Howell gave himself a great chance to claim a seventh European Tour title after opening with a birdie and picking up three shots in four holes to turn in 33, but his form deserted him on the inward half and he had to be content with a 69 – making him the only man in the field to shoot four sub-70 rounds.
Wall made his second eagle of the week at the opening hole and added birdies at the fourth and eighth either side of a bogey at six, and he vaulted into a share of the lead on 16 under after back-to-back birdies at 13 and 14.
But he could not respond from his error at the next as he returned a four-under 68, while South African journeyman Coetsee struggled to build any momentum after labouring to the turn in 37 and making his second bogey of the round at the 12th.
He did salvage a 71 with birdies at 14 and 18 to join the share of second place alongside his compatriot Van Zyl, who carded three straight birdies from the sixth and picked up two more at the 11th and 18th to complete a faultless 66.
Ireland’s Phelan had been first into the clubhouse on 15 under after a remarkable round which included six birdies over the first eight holes, and he also made a pair of twos at both par-threes on the inward half around a bogey at 14.
In-form South Korean Byeong Hun An carded four birdies and finished with an eagle-three to cap a bogey-free 66 which earned him a share of seventh place, and he has finished no lower than 13th in his last four European Tour starts.
An was joined on 14 under by home pair Chris Swanepoel (69) and Jacques Blaauw (70), while defending champion George Coetzee’s challenge ended with three consecutive bogeys around the turn as a disappointing 73 left him seven shots behind the champion.