Olesen - who has previously enjoyed success in Australia as the winner of the 2014 Perth International - chipped in at the eighth as the pair amassed two eagles and eight birdies.
They finished a dream day at 12-under-par, three shots clear of China's Wu Ashun and Li Haotong, with first-round leaders Rafa Cabrera Bello and Jon Rahm from Spain a stroke further back in outright third place.
Americans Rickie Fowler and Jimmy Walker were in a tie for fourth at seven under.
Australians Adam Scott and Marc Leishman were all but out of contention after battling to a four-under 68.
It left the local favourites 10 shots off the pace in a tie for 18th as they struggled to build any real form on a cold, windy day at Kingston Heath.
Kjeldsen said the strength of his partnership with Olesen was their contrasting styles.
"Temperament-wise I don't think we're that different but game-wise we're very different," said the 41-year-old, who has won four times on the European Tour.
"Thorbjorn is very flashy, he hits it very far off the tee and overall just has an amazing game, whereas I'm like a train - I arrive on time but without too much of the flashy stuff."
Both Danes had previously shot 61s in individual strokeplay, with Olesen admitting the magical figure of 59 crossed his mind after a fifth successive birdie on the 14th.
In the end they could only manage one more birdie - on the 18th - for a 12-under 60.
"I didn't know what the par was on this course but I thought 13 under would definitely make it," said the 26-year-old Olesen.
"I had it in my mind and I was still trying to play the same golf and be aggressive.
"We came up one short but Soren hit an amazing shot into 18 and it was great to finish that way."
The format switches back to alternate-shot foursomes on Saturday before concluding with another round of best-ball fourballs on Sunday.
- With AAP
