Darren Clarke, a two-time runner-up here, carded a 5-under-par 66 to share third place with Miles Tunnicliff.
Scotland's Raymond Russell is one stroke further back at minus-4. He stands alongside David Bransdon, Andrew Butterfield and Jose Maria Olazabal, who shared second place here in 1989.
Edfors got off to a flying start with birdies on one and two. After a par on the third, he moved to 3 under with a birdie on the par-4 fourth.
The Swede came right back to birdie No. 5 as well. Edfors tripped to a bogey on the par-5 sixth, but atoned for that mistake with a birdie at eight.
Edfors, who earned both of his tour wins earlier this year, got to 5 under as he birdied the 10th. He dropped a shot on 12, but got that shot back with a birdie at the next.
The 30-year-old moved to minus-6 with a birdie on the par-4 15th. Edfors stumbled to the third bogey of his round at the 16th, then closed with a birdie at the last to grab share of the lead.
Drysdale started on the back nine and birdied his first hole. He carded his second birdie on the par-5 13th, then parred the final five holes of his opening nine.
The 31-year-old Scotsman drained a birdie effort on the first and got to 4 under with a birdie at the par-5 third. Drysdale closed with back-to-back birdies from the eighth to end alongside Edfors.
Englishman Luke Donald leads a group tied in ninth place at 3-under-par 68. Among the 13 others at minus-3 are Jamie Donaldson, Hale Irwin, Raphael Jacquelin, Barry Lane and Carl Pettersson.
Defending champion Tim Clark and Order of Merit leader David Howell are part of a large group tied in 23rd at 2-under-par 69.
Eight-time Order of Merit winner Colin Montgomerie is part of a logjam in 81st at 1-over-par 72.