Karlsson overcame two early bogeys Thursday while McIlroy also had seven birdies and two bogeys on the day to share the lead.
Jean-Baptiste Gonnet, Richard Finch and Gareth Maybin are tied for third at 4-under with another group of three in at 3-under 69. Tiger Woods, who had two birdies and 16 pars Thursday, is among 11 players tied at 2-under.
Karlsson, playing the second nine of the Abu Dhabi Golf Club first Thursday, countered bogeys at 10 and 12 with birdies at 11 and 13. He closed the side with two birdies and climbed into the lead with three birdies in a five-hole span over Nos. 4-8.
McIlroy, also starting at the 10th hole, had three birdies in his first four holes before a bogey at 14. He had a 5 at the par-4 17th but came back with a birdie at 18.
He returned to 3-under with a second-hole birdie and added birdies at Nos. 7 and 8.