Horsey posted six birdies in his opening 12 holes to put pressure on Olesen but the 26-year-old hit back with three birdies in four holes from the 12th to card a two-under-par 69 and win on 20 under.
Horsey and China's Li Haotong both shot 65s to finish joint second on 17 under.
"I actually slept all right the last couple of days," Olesen told the European Tour website (www.europeantour.com), when asked how he felt about protecting his vast lead.
"It was a weird feeling. I knew the guys today were able to shoot a low number so I had to make a few birdies. After nine holes guys were shooting really low numbers so all of a sudden there was a lot of pressure on.
"I felt like I kept it pretty steady. Obviously, the last four holes were tough mentally."
Olesen had won the 2015 Alfred Dunhill Links Championship after a run of 13 missed cuts in 18 events, which was a similar story to his success at Antalya's Regnum Carya Golf and Spa Resort after he had made only three cuts in his previous 12 events.
(Writing by Ian Chadband; Editing by Clare Fallon)
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