Both men carded eight-under-par rounds of 64 on the Oceanico Victoria course to lead alongside Dutchman Maarten Lafeber.
Another Swede, Alexander Noren, was a shot further back, with Finland’s Mikko Ilonen.
Paul McGinley was the best-placed Irishman on six under, alongside England’s David Horsey.
Karlsson and Edfors both covered the Oceanico Victoria course in unblemished rounds including eight birdies.
Karlsson was a model of consistency after starting his round on the 10th, picking up birdies on his first, the 12th, the 16th and the 17th.
He was equally efficient coming back, picking up shots at two, three, four and six, and found the conditions to his liking.
“I think with this kind of set-up with not so much rough, that’s very often what we play in Sweden,” Karlsson said.
“It’s a bit similar to Swedish golf, and the speed of the greens as well are not super fast.
“I think we are very used to playing this type of golf on our home courses where we grew up.”
He added: “If the wind stays down, this is one of the courses you can shoot, especially now when the rough is down, as well. So without wind, the (record) 59 is possible.”
Edfors did much of his good work in his back nine with five birdies to add to the three he produced on the way out.
Lafeber might have held the lead on his own but for a double bogey on the par-four 18th, which ruined an otherwise impressive round that included nine birdies.
After birdies on his opening three holes the Dutchman has seemingly lost the momentum in his round when he shot a six at the 18th.
But the 35-year-old recovered impressively as he added a further six birdies on his inward nine to take a share of the lead at a course where 24 under par has been the average winning score.
Noren also experienced a day of ups and downs in his round with seven birdies, one eagle and two bogeys.
Of Europe’s Ryder Cup heroes, England’s Ross Fisher and Edoardo Molinari were best placed after shooting four-under-par rounds of 68.
Miguel Angel Jimenez was two shots further back, while Francesco Molinari looked set to miss the cut after carding a two-over-par 74.