The South African golfer shot a 6-under-par 65 in the final round to finish at 13-under 271 and enter a playoff with Garth Mulroy and Magnus A. Carlsson.
Mulroy and Carlsson, who each posted 66 in the final round, missed birdie attempts on the second playoff hole.
Sterne previously won the tour's 2004 Madrid Open and 2007 Celtic Manor Wales Open.
Mark Murless, who had led or been tied for the lead after the first three rounds, closed with a 73 and ended up in a three-way tie for fifth place.
Celebrity Families of 2014 [PHOTOS]