The Swede has never managed a top-50 finish in six visits to the West Course, but six birdies and a solitary bogey moved him within two shots of leader Luke Donald.
"I've always struggled here but I think it's a bit easier with the new greens," said Edfors, who finished second in Andalucía earlier in the year. "I struggled on the greens the first couple of years I was here, but still, it's a really tough golf course. There's trouble left and right on almost every hole so you have to keep it in the middle of the fairway and keep hitting good iron shots, otherwise it's going to come back and bite you.
"I've been playing pretty nicely. I'm struggling a little bit with the putter. I have a new putter this week and worked really well today, if I can keep putting like I did today, I'll be really dangerous. It's a different Odyssey putter and went back to my two-thumb grip, so really happy with that switch today."
Wet and windy conditions made Edfors effort all the more impressive, as he joined Italian teenager Matteo Manassero in a share of second place.
"I must have had my rain jacket off and on 15 times today," he added. "You get some really nice spells and you get the biggest gusts and pouring rains, so it was tough out there, I managed to play well the whole way and nice with two finishing birdies."