Blixt, 39, missed the cut on the Korn Ferry Tour last week, but the Swede got off to a quick start at TPC Deere Run with an eagle on his second hole.
After making the turn in 2-under 33, Blixt added a pair of birdies before draining a 43-foot eagle putt on the par-4 14th hole.
That propelled Blixt to three more birdies over his final four holes, capping his 660th official round on the PGA Tour by carding a 29 on his back nine. Blixt hit only six of 14 fairways, but missed only two greens.
"Sixty-two doesn't happen very often on the PGA Tour, at least not for me," Blixt said. "I'm very happy about it. Extremely happy about it."
Several players made late runs at Blixt's score from the morning, but multiple chasers faltered late. That included Grayson Murray, who started on the back nine and reached 8 under through 13 holes before settling for a 7-under 64 following a bogey on his final hole.
Cameron Young, the top-ranked player in the field at No.19 - 823 spots higher than Blixt - birdied the 17th hole to get to pull even with Murray. However, he found the rough off the tee on 18, narrowly avoided the water with his third shot and salvaged bogey to settle for a tie for third at 6 under.
Greyson Sigg, Adam Schenk, Nate Lashley, Richy Werenski and South Africa's Garrick Higgo also shot 6-under 65.
Blixt is a three-time winner on tour, the most recent victory coming at the 2017 Zurich Classic of New Orleans, where he partnered with Australian star Cameron Smith to win the team event.
His last individual victory was at the Greenbrier Classic in 2013. The following year, he reached a career-high world ranking of No.33 after tying for second at the Masters.
Thursday's round tied Blixt's 62 shot during the third round of the 2015 Wyndham Championship. It also came after Blixt missed the cut by three shots at last week's Memorial Health Championship on the KFT - the third consecutive event at which he had failed to make the weekend.
"I think I found something this week after playing the Korn Ferry last week," he said. "At this point, when you don't have that much confidence in your game and you find something, you just kind of go out and swing at it. That's what happened."
This is Blixt's ninth start on the PGA Tour this year, with his best finish to date a T20 at the AT&T Pebble Beach Pro-Am. He has struggled to get into PGA events and worked heavily with his swing coach during a recent six-week break.
"I kind of came to the point in my season where it's so late that I don't feel any pressure anymore, really," he said. "Golf is weird. Tomorrow I can shoot 100, I feel like, but today was a great day."
Harrison Endycott (68) is Australia's leading challenger and tied 23rd.
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