The 26-year-old ended his round with a flourish, reeling off four birdies and an eagle in his last six holes to finish with a 15-under total of 127 at the Regnum Carya Golf and Spa Resort.
"Yesterday was a great putting display and today I played better and still putted great," triple European Tour winner Olesen told reporters.
"I feel like I've been up there in contention in a lot of big events so I feel pretty comfortable. I have to keep being aggressive, keep going after some of the pins and try to make birdies -- that's the only way I can win."
Spain's Adrian Otaegui shot a 63 to share second place on 133 with Thongchai Jaidee (66) of Thailand in the opening event of the tour's Final Series that also includes the Nedbank Challenge in South Africa and the DP World Tour Championship, Dubai.
U.S. Masters champion Danny Willett, the only player in the top three of the money list competing in Antalya after number one Henrik Stenson and third-ranked Rory McIlroy opted out, struggled to a 74 for 143.
(Writing by Tony Jimenez; Editing by Toby Davis)
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