Svensson, who has one PGA Tour victory to his name, carded an 11-under-par 60 at TPC Twin Cities to lead by two over American Sam Stevens and Denmark's Thorbjorn Olesen.
The highlight of Svensson's round came on the closing hole when he holed a 48-foot eagle putt to add to the nine birdies he'd already made.
Chris Gotterup, fresh off a third-place finish at last week's British Open and a win at the Scottish Open the week before, sat three shots off the lead alongside Chad Ramey and Matti Schmid. One stroke behind them were Zac Blair, Chris Kirk, Jake Knapp, and Brendan Valdes, while Rickie Fowler and Emiliano Grillo were among a group tied at six under.
But the day belonged to Svensson, whose lone PGA Tour win came at the 2022 RSM Classic and who had recorded just one top-25 finish in 21 starts this season.
"I had a great range session today. Just really putted amazing, I made a bunch of breakers. It was probably my best putting round I ever had," said Svensson, who also holed a 40-foot birdie on the 11th hole and a 34-footer on the fourth.
Stevens had a chance to shoot 59 with an eagle on the par-5 18th, but his second shot from 246 yards found the water in front of the green. The miscue led to his only bogey of the day, though his 62 still marked the lowest round of his PGA Tour career.
"I have a pretty big gap between my 3-iron and my 3-wood, and I hit a terrible shot. I thought if I hit a 3-wood, it was just going to fly to the back of the green, and I kind of had to hit a 3-iron perfect to even cover the water. But I figured that was my best chance to shoot 59, so I gave it a go," he said.
Fowler and Grillo both need strong showings to boost their chances of qualifying for the 70-man field at the first FedExCup playoff event in two weeks. Fowler began the week at 63rd, while Grillo sits at 71st.