Dutchman Maarten Lafeber also joined the Swedish pair in a three-way tie for the lead.
All three shot eight-under-par rounds of 64 at the Oceanico Victoria Golf Course with another Swede, Alexander Noren, and Finland’s Mikko Ilonen a shot further back.
Karlsson and Edfors both hit perfect rounds that included eight birdies in conditions which proved to their liking.
“I think with this kind of set-up, with not so much rough, that’s very often what we play in Sweden,” Karlsson told www.europeantour.com.
“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.”
Karlsson started his round on the 10th, picking up birdies on his first, the 12th, the 16th and the 17th. Coming back he picked up shots at two, three, four and six.
Edfors produced five birdies in the back nine to add to the three he earned on the way out to hold off Lafeber, who might have held the lead on his own after nine birdies but for a double bogey on the par-four 18th.
Of Europe’s Ryder Cup stars, England’s Ross Fisher and Italy’s Edoardo Molinari were best placed after shooting four-under-par rounds of 68.
Spaniard Miguel Angel Jimenez was two shots further back, while Francesco Molinari looked set to miss the cut after carding a two-over-par 74.
David Horsey was the best-placed Englishman on six under, alongside veteran Irishman Paul McGinley.