Madsen started the final round one stroke off Charl Schwartzel's lead but came through with a bogey-free round Sunday for the win. It was his fourth professional title overall, with the other three coming in the Nordic League.
Madsen had a spate of four bogeys in a five-hole span of the first round Thursday but had only three bogeys the rest of the week and finished at 19-under 269. His steady second nine Sunday, which included birdies at Nos. 13, 15 and 16 and six pars, clinched the win.
South Africans Jbe Kruger, who had a 65 Sunday, and Hennie Otto, with a 68, tied for second at 17-under. Schwartzel, who had a triple bogey and a double bogey Sunday en route to a 1-under 71, tied Marco Crespi for fourth at 16-under. Crespi turned in a 2-under 70 Sunday.
Schwartzel seemed on his way to the tournament title when he had three birdies in the first four holes Sunday but he erased all that with a 6 at the par-3 sixth hole. Madsen, meanwhile, had birdies at Nos. 2 and 7 that moved him into the lead.
Schwartzel dropped out of contention with a double-bogey 6 at the 10th hole.
Otto had consecutive birdies over Nos. 12-14 that had him 20-under for the tournament but he stumbled with a bogey at the par-5 15th and a double bogey at 16.
Kruger was 5-under in a four-hole span late in the round but didn't get closer than two strokes of Madsen.