The Danes teed off four strokes adrift of overnight leaders Spain on another gusty day at the sandbelt course but finished with Kjeldsen sinking a three-foot putt on the 18th for the pair's eighth birdie in a brilliant 12-under round.
They head into Saturday's foursomes with a handy buffer over second-placed China, with Spain a further stroke behind on eight-under.
"I was trying to play solid, Thorbjorn was playing exceptional," beamed 41-year-old Kjeldsen next to his partner Olesen, 15 years his junior.
"It's one of the best courses I've ever played ... You could play this course every day for the rest of your life."
None of the other 28 nations in the field came close to the dominant Danish pair, who also grabbed two eagles, but China's Wu Anshun and Li Haotong were well placed after combining for a 65 on another solid day.
Joint second overnight, the United States slipped to fourth with France, England and Italy on seven-under.
Americans Rickie Fowler and Jimmy Walker combined for 67 but were disappointed with a yield of five birdies.
"A few more would have been nice to go into the weekend," said world number 12 Fowler. "We haven't played our best golf yet or anything close to it."
Australian Adam Scott's hopes of defending his 2013 team title, won with Jason Day at Royal Melbourne, dimmed further as he and Marc Leishman again struggled to gel.
Five off the pace overnight, the pair rolled in six birdies but both stumbled with bogeys on the seventh and 16th holes and head into the weekend 10 strokes behind the Danes after a 68.
"I certainly didn't play the way I would've liked," said Leishman. "But that's golf and it can do that to you.
"I'm still staying positive, hoping we've saved all of our good stuff for the weekend."
Ireland's Shane Lowry and Graeme McDowell also have work to do, the pair shooting a 69 to be nine strokes adrift.
Kjeldsen and Olesen parred their first two holes before their round roared into life with an eagle on the par-four third followed by birdies on the next two holes.
Another eagle came on the par-five eighth before their game went up another level at the turn, as they started the back nine with five consecutive birdies before Kjeldsen capped the round in style.
"I'm like a train ... I arrive on time," Kjeldsen joked as he compared his safe game with Olesen's more aggressive approach. "It's a good combination."
(Reporting by Ian Ransom; Editing by Peter Rutherford)
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