They were tied with Maarten Lafeber of the Netherlands, who had six birdies on his last nine holes to help make up for a previous double bogey on the 18th.
Alexander Noren, another Swede, was one shot back in fourth.
Only one player among the afternoon starters managed to break into the top five on the leaderboard, Finland’s Mikko Ilonen making light of the bumpy putting conditions to complete a 65 and join Noren at 7 under.
European Ryder Cup team member Edoardo Molinari was also one of the late starters and shot a 4-under 68.
“The greens were uneven,” the Italian said. “I had one stupid three-putt from 20 feet on the seventh green. But when that happens it important to think about the putts you have made rather than the ones you miss.”
However after his eight birdie round, which contained no bogeys, Karlsson believed another factor could play a big part in the chase for Sunday’s $704,000 top prize.
After a week of heavy rain, the course is playing much longer than its nominal 7231 yards.
“The fairways are quite soft and it is a big hitters’ golf course,” the 41-year-old Karlsson said. “If you hit it long you can still get up in two at all of the par fives but the shorter players are having to lay up short. So it is suited to the big hitters.”
It was a view reinforced by Edfors, who said: “If the wind stays down, this is one of the courses you can shoot very low, especially now when the rough is down as well. So without wind, the 59 is possible.”
Lafeber could have got close to becoming the first player to shoot 59 in a European Tour event. His round included 11 birdies but a double bogey after he found water by the 18th green – his ninth hole of the day – cost him the outright lead.