The Dane was cruising along at three-under for the first day at the Pretoria Country Club before he fired a hole-in-one at the eighth – his 17th – and then closed with an eagle-three to cap a seven-under 63.
Madsen, who finished third at last week’s Africa Open, started with a birdie on the 10th and picked up another shot at 16 in a back-nine 33 before rolling in a 30-foot putt for a three at the first hole.
He responded to his only mistake of the round at the fourth with another birdie at the sixth, and his wedge to the 135-yard eighth pitched beyond the flag and spun back into the cup for a superb ace.
Madsen then knocked a sublime second to 12 feet at the next and rolled in the eagle putt to set a testing target in the clubhouse, a score which only Horsey was able to match after he returned a faultless seven-birdie round.
???The last couple of weeks I???ve been hitting some shots really close and I actually said to my caddy last week that a hole-in-one is on the cards pretty soon,??? Madsen told the European Tour website.
“Luckily for me it came today. I hit a fantastic shot, I couldn???t hit it better, and it spun back into the hole. That was only my second hole-in-one and it???s really special to have one in competition on the European Tour.
“When you stand on the next tee you???re pretty pumped and confident. I succeeded in gathering my thoughts and hit a really nice drive and then a great second shot and then sank it, which was a fantastic way to finish. It was the kind of thing you dream about, but don???t expect.
???Today was a great day and I had a lot of fun out there.??I???ve found something in my game that???s working and I???ve been pretty consistent.???
Horsey kick-started his challenge with three birdies in four holes in an outward 32, and picked up further shots at 12, 14, 16 – where he drained a huge 40-foot birdie putt – and 17 to join Madsen at the top of the leaderboard.
The pair are one shot ahead of in-form South African Wallie Coetsee, who pitched in for an eagle at the 12th, and Australian veteran Brett Rumford, while Raphael Jacquelin birdied his final three holes to hand in an impressive 65.
The Frenchman was later joined on five under by home trio Dean Burmester, Keith Horne and Merrick Bremner, while Africa Open champion Trevor Fisher Jnr continued his fine run of form with a solid 66.
Defending champion Ross Fisher opened with a 69 that featured 16 pars, an eagle at the 12th and a bogey at 16, but European Ryder Cup captain Darren Clarke and two-time 2015 winner Andy Sullivan both have work to do to make the cut after they carded erratic 71s.