England's David Horsey had six birdies in his opening 12 holes to put pressure on Olesen but the Dane responded with three birdies in four holes to card a three-under 69 and win on 20 under par.
Horsey and China's Li Haotong both shot 65 to finish second on 17 under.
Masters champion Danny Willett failed to take top spot in the Race to Dubai.
The Englishman needed to finish fifth to move ahead of Open winner Henrik Stenson but was joint-68th after a disappointing final round of 75.
It was Horsey who had seemed the most likely to upset Olesen, holing five birdies to reach the turn in 29, while the Dane three-putted the ninth to card just his fourth bogey of the week.
But Olesen responded with birdies at the 12th, 14th and 15th and although he bogeyed the 16th, pars on the final two holes saw him claim victory.
He built his win on the back of course record 62 in the second round after missing the cut in eight of his 10 previous events.
He said: "The last three or four months have been poor and I didn't feel comfortable at the end, but I got over the line.
"I knew they had cut the lead to a couple of shots and it puts pressure on you. The last four holes were really difficult."
Thorbjorn Olesen rallied to claim the Turkish Open title by three shots - after briefly seeing his seven-stroke overnight lead reduced to just one.