Horsey was one shot ahead of defending champion Rhys Davies of Wales and Dutchman Jaco Van Zyl at the par-4 18th, but stumbled to a double bogey that left him at 13-under 274.
Davies (69) missed a 4-footer for par that would have given him the win and Van Zyl (68) made par on the last to join the playoff.
All three parred the first playoff hole before Horsey won it on the second.
“I’m relieved more than anything,” Horsey said. “I made hard work of that coming down the last.”
Horsey had his hole-in-one at the par-3 second, giving him the lead after being tied with Davies overnight.
“It is not very often that you get off to a start like that on the last day of a tournament, especially when you are in a position to win,” Horsey said. “Obviously there is a certain amount of luck involved in a hole in one, but it really set me up for the rest of the day.”
Horsey became the fourth Englishman to win the event, after Peter Townsend (1978), Martin Gates (1994) and Roger Chapman (2000).
Davies missed an easy putt on the last hole that would have given him the victory.
“I couldn’t believe Rhys missed that putt to win, to be honest,” Horsey said. “If we had been playing match play I would have given him that putt because he is one of the best putters in the world.”
Thomas Bjorn of Denmark set a course-record 62 to finish at 6 under in 15th place.
“I played well even with a bogey and a three putt,” the former Ryder Cup star said. “It was just one of those days when I holed my fair share of putts and never made any big mistakes.”