All three shot eight under par rounds of 64 at Oceanico Victoria Golf Course on a day when benign conditions paved the way for some impressive scoring.
CommercialBank Qatar Masters presented by Dolphin Energy champion Karlsson was European Number One in 2008 before eyesight problems saw him endure a torrid 2009.
But the 41 year old returned to the winner's circle at the start of the year and currently sits 25th in The Race to Dubai.
He carded eight birdies in a bogey-free round on a course where he has previously finished second and third.
"You can be very aggressive and the par fives when I hit my driver good, I can get up on all of them, and today was quite easy," said Karlsson.
"The par fives, is obviously key on this golf course, because if you're playing the par fives well, you have a chance to make a good score, and the par fives suit my eye very well."
Despite his impressive start Karlsson was quick to play down talk of an 11th European Tour title.
"Three days to go, I'm very happy to put in a great score and then we go from here," he said. "Just very pleased with today, and that's one of my goals, is to play well every day as a separate tournament, but if I can put up another three at least, maybe I have a chance.
"I try to play every tournament as a separate event. This is the tournament I'm playing. It doesn't matter if I'm first on The Race to Dubai or 150. This event is this event only - I can't do more."
His compatriot Edfors recorded all three of his European Tour wins in 2006, and was pleased to take advantage of the calm conditions on the Algarve.
"Barely no wind and it's playing really soft," he said, before adding that a first 59 in European Tour history was a possibility this week.
"I played decent on the front nine, I had a little slow start. I had a couple good chances that I missed but then after that, I holed really every chance I got there, and the putting was just fantastic. I didn't hit it all that close actually today but I holed a lot of 15 20 footers for birdie."
Lafeber's round was all the more remarkable considering it contained a double bogey at the 18th - his ninth - but the former Dutch Open winner was in fine form as he registered 11 birdies.
On a good day for the Swedish contingent, Alexander Noren shot a seven under 65 to share fourth place with Finn Mikko Ilonen, with England's David Horsey and Ryder Cup Vice Captain Paul McGinley a shot further back.