Svensson also made nine birdies and did not drop a shot in the lowest round in the tournament's seven-year history to lead over American Sam Stevens and Dane Thorbjorn Olesen.
As Australia's challenge failed to materialise, the Canadian tied the TPC Twin Cities course record set by Paul Goydos at the 2017 3M Championship on the PGA Tour Champions.
Chris Gotterup, who finished third at last week's British Open and won the Scottish Open two weeks ago, is three shots back along with Chad Ramey and Matti Schmid.
Zac Blair, Chris Kirk, Jake Knapp and Brendan Valdes are another shot back, with Rickie Fowler and Emiliano Grillo among those at six under and four strokes off the pace.
Svensson's lone tour win is the 2022 RSM Classic. The 31-year-old has one top-25 finish in 21 starts this season and has missed 11 cuts.
"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," he said after needing just 25 putts, including a nearly 40-foot birdie on the 11th hole and a 34-footer on the fourth.
His career-best 60 is the second-lowest score on the PGA Tour this season. Jake Knapp shot 59 at the Cognizant Classic in February.
Stevens could have shot 59 with an eagle on the par-5 18th, but instead he put his second shot from 246 yards into the water in front of the green, leading to his lone bogey and a 62 that was still his lowest round on tour.
"I have a pretty big gap between my three iron and my three wood, and I hit a terrible shot," he said.
"I thought if I hit a three wood, it was just going to fly to the back of the green, and I kind of had to hit a three iron perfect to even cover the water. But I figured that was my best chance to shoot 59, so I gave it a go."
Fowler and Grillo are among a group of 18 players who rank between 60th and 80th in the FedEx Cup standings, needing a strong performance to help secure spots in the 70-man field for the first playoff event in two weeks.
Fowler entered the week at No. 63 and Grillo is No. 71.
"At the end of the day, good golf solves a lot of things," Fowler said.
Adam Scott, once again, is the leading Australian, some nine shots off the pace in a tie for 77th after opening with a two-under 69.
Karl Vilips (70), Cam Davis (71), Aaron Baddeley (73) and Harrison Endycott (73) all need strong second rounds to make the halfway cut.
With AAP
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