The 22-year-old Swede, who led by two shots overnight, totaled 12-under 204 at Doha Golf Club. One of the most improved players on the European Tour since 2006, Edfors had four birdies and one bogey.
Andrew Coltart of Scotland, the 1998 champion, had nine birdies and two bogeys in a 65 to trail by a shot.
Former champion Henrik Stenson of Sweden (67) and Charl Schwartzel of South Africa (69) are tied for third, two strokes back.
Former champion Adam Scott of Australia, Ross McGowan of England and first-round co-leader Anton Haig of South Africa was another shot back and tied for fifth.