A stunning round of 60 in the fourballs on Friday had given the duo a three-shot advantage, and they extended that with five birdies and three bogeys in a 70 in the foursomes to reach 14 under par.
"We showed yesterday that a really low score is possible out there in the fourball. I had a seven-shot lead in Turkey and it got down to one shot very quickly, so I know how quick this game can go sometimes," said Olesen.
"It's definitely not going to be easy tomorrow. There's a lot of great players here and a lot of birdies out there. It's a four shot lead, which is really nice, but it's not going to be easy."
The United States pairing of Jimmy Walker and Rickie Fowler emerged as their nearest challengers with a round of 69, but they face an uphill battle to deny Denmark their first World Cup title.
It's not an impossible task with Germany achieving the feat at the 2006 World Cup of Golf in Barbados. The German team of Bernard Langer and Marcel Siem, made up five shots on leaders Sweden to grab the title in a play-off against Scotland, while the Swedes finished a shot further back in third.
Team USA will play alongside Team Denmark in the final round, they tee off at 11.25am.
"It would be nice to be out front or a little closer, but with where we were coming into today, just putting up a solid round of golf was that we wanted to do," said Fowler. "We did that and we gave ourselves a chance going into tomorrow.
"It's going to take some good golf and some birdies obviously, but it will be nice being in that final group to know exactly where we stand."
Wu Ashun and Li Haotong stumbled badly with an opening double bogey and bogey in their opening two holes at Kingston Heath Golf Club before recovering courageously with birdies on four, five and 11 to end the day in third place on nine-under-par 207
Wu was delighted with the way he and Li fought back following their stuttering start.
"We had some trouble from the beginning but we played very good after that," said Wu.
"We talked a bit and we said 'let's go, new tournament right now, new hole right now.'
Nothing can be worse after two holes. We still had a lot of holes, a lot of chances and we played simple golf and made some birdies."
After narrowly missing birdie chances on the first and second, Denmark dropped their first shot in 25 holes on the third as Kjeldsen found the sand with the second shot but they bounced back with a pair of birdies.
An excellent approach from Olesen had left Kjeldsen with little to do on the fourth and the 26 year old then drained a 12-footer for a five-shot lead.
Another birdie came on the tenth and after the pair did well to drop just a single shot after a ragged Olesen tee-shot on the 11th, he made amends with an excellent one on the short 13th to set up a gain. A three-putt bogey on the 17th then slightly took the gloss off the round.
The United States three-putted the first but bounced back with a birdie on the second and when Walker made another good putt on the fifth, they were alone in second.
A bogey was to come on the seventh but Walker was putting beautifully and back-to-back birdies on the eighth and ninth were followed by another gain on the 17th as the Americans search for a 25th title.
The Japanese pair of Hiedki Matsuyama and Ryo Ishikawa came home in 35 in a 71 while Frenchmen Victor Dubuisson and Romain Langesque went round in 72 with the help of an eagle on the eighth.
Rafa Cabrera Bello and Jon Rahm signed for a 73 to also sit at seven under, a shot clear of Italy and two ahead of Ireland, New Zealand and Sweden.
The final round of the ISPS HANDA World Cup of Golf, which will be played in the fourball format, gets underway at 8.23am, with the last group due out on course at 11.25am.
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What's on this week / 25th - 31st January 2017
Discover what's on in the world of golf and which Aussies are in action this week