Uihlein and Madsen were tied at 15-under entering the final hole at Club de Golf do Santo da Serra. Denmark's Madsen ran into problems and could manage only a double-bogey 6, while the American carded a par for the victory at 15-under 273.
Madsen shot to final-round of 67 and ended in a tie for second with third-round leader Mark Tullo (71).
Craig Lee (71) finished fourth at 12-under.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys