The 24-year-old from Nuneaton closed with a trio of threes over the Lansdowne course in a three-under 69 and pipped Wentworth's Steven Brown to the title by a single shot on a six-under 282.
Sullivan, who led at halfway, had his challenge blown off course in the strong winds with a third round 77 but he responded in superb style as Brown piled the pressure on with a closing 70 for 283.
A 10-foot putt for birdie on 16 kick-started Sullivan's late surge and, having rolled in a 20-footer for eagle on 17, the Walker Cup hopeful launched a superbly flighted seven-iron into four-feet on the last to snatch the crown.
"It was a struggle from the word go today in the conditions but I just kept going and didn't give in," he said. "These finishes can happen in golf, although it's quite rare, and it was great. The Walker Cup is a huge target for me and this is a step in that direction."
Kirkhill's Paul Shields continued to knock on the door of a major breakthrough as he took third place on 286 after a pair of 72s.
The 20-year-old, twice a runner-up in the Scottish Boys' championship and beaten to the South African Amateur crown earlier this season, had moved into a share of the lead during the afternoon but his hopes were thwarted when he found the trees on 18 and took a bogey-five.
"It was a bit of a disappointing end but I'm happy that I got myself into contention again," said Shields. "As long as I keep knocking on the door, then hopefully that win will come."
Perth's Daniel Young notched one of his best results on the circuit with a share of fourth on 288 while Blairgowrie's Glenn Campbell, the Scottish matchplay champion in 2005, tied fifth on 289.