JOHANNESBURG, November 24, 2013 (AFP) - Belying his 244th world ranking the 25-year-old Dane won the EPGA's opening 2014 Race To Dubai event by two shots after a final round 67 for a 19 under par total of 269.
South African Jbe Kruger earned a share of second with a 65 to join his compatriot Hennie Otto at 17-under par.
Another local hope, Carl Schwartzel, let slip his one shot overnight lead in a fourth round marred by a triple bogey at the par three sixth.
The Johannesburg native, aiming to win the South African Open for the first time, made up some ground on the back nine but signed for a 71 for fourth, on 16-under par, with Marco Crespi of Italy.
Madsen described the outcome as "amazing" and added: "It's a cliche to say it hasn't sunk in - but it hasn't.
"I'm so happy. Coming here I expected to play well but not to be standing here talking as the winner."
"It's been an amazing day," said Madsen, who had five birdies in all during a blemish-free round."
Despite going round with 2011 Masters Tournament champion and eight-time Tour winner Schwartzel, Madsen said: "I definitely felt like I could still win, but he looked like he was going to go off and I was just trying to hang on and maybe stay in two or three shots and give myself a chance.
"I had a great back nine but unfortunately for him he struggled. On a couple of holes he had some bad breaks. Luckily for me I was there to capitalise and I did with some nice birdies down the stretch."
Leading scores after the final round of the South African Open on Sunday (GBR & IRL unless stated, par 72):
269 - Morten Orum Madsen (DEN) 67 66 69 67
271 - Hennie Otto (RSA) 72 66 65 68, Jbe Kruger (RSA) 65 70 71 65
272 - Marco Crespi (ITA) 65 67 70 70, Charl Schwartzel (RSA) 67 65 69 71
273 - Alejandro Canizares (ESP) 69 67 69 68
274 - Johan Carlsson (SWE) 69 70 68 67, Trevor Fisher Jnr (RSA) 70 67 73 64
275 - Warren Abery (RSA) 68 71 68 68
276 - Christiaan Basson (RSA) 66 68 71 71, Garth Mulroy (RSA) 70 67 70 69
277 - Andy Sullivan 71 68 68 70, Martin Du toit (RSA) 70 70 68 69, Jean Hugo (RSA) 71 67 70 69, Peter Karmis (RSA) 69 72 67 69, Jaco Van Zyl (RSA) 71 70 66 70
278 - Merrick Bremner (RSA) 73 69 67 69, Thomas Aiken (RSA) 70 67 71 70, Peter Whiteford 71 68 70 69, Daan Huizing (NED) 68 69 73 68, Thomas Levet (FRA) 69 70 70 69
279 Michael Hollick (RSA) 75 67 68 69, Ulrich Van Den Berg (RSA) 70 66 71 72, Retief Goosen (RSA) 66 71 70 72, Ross Fisher 71 69 68 71, Jorge Campillo (ESP)