The 25-year-old Canadian drilled a putt for his seventh birdie on the 18th green to move a shot clear of American Andrew Putnam, who earlier in the day used a red-hot putter to card a 62 at Waialae Country Club in Honolulu.
Svensson, who ignited his flawless round with an eagle at the par-five ninth, attributed the lowest round of his career to his putting.
"My speed was great," he told Golf Channel. "I was around the hole, I hit 17 greens or something like that, so I gave myself a lot of opportunities and I came out with a 61."
Svensson said he was pleased with how he played but will not be getting ahead of himself as he looks to land his first PGA Tour title.
"Just stay patient. You hear a lot of people say that," he said.
"Pars are great out here. The odd birdie here and there is great. So I'm just going to go out there and have fun tomorrow and enjoy it."
While relative unknowns like Svensson and Putnam were running in birdie after birdie in brilliant sunshine, Spieth managed just one in what passes for winter in the Pacific tropics.
The three-times major champion is seeking a return to the peak after the first disappointing season of his career, and warned on the eve of that it could take a while.
Thursday's evidence suggested that could be the case.
"I went through a couple of different swings today," the Texan told reporters.
"I don't feel like I've been in this situation before."
"I'm over the ball and not comfortable. It's going to happen (at some stage of) your career."
Spieth said he was confident he would get back to where he thinks he should be.
"I'm not worried about it... As long as I don't let it get to me like I did last year at times."
Remembering one of golf's new 2019 rules was also proving a work in progress for Spieth, who on two separate occasions dropped his ball from shoulder height when taking free relief, rather than the knee height now required.
Fortunately a rules official reminded him of his error before he had played his next shot.
Had they not, it would have been a one-shot penalty.
(Reporting by Andrew Both in Cary, North Carolina and Rory Carroll in Los Angeles, editing by Nick Mulvenney)