Levet and Olesen were tied at 7-under heading into the final hole and Levet finished with a a two-putt par. Olesen, however, saw his two-footer for par lip out, leaving Levet in the lead.
Levet had to wait in the clubhouse for third-round co-leader Mark Foster to finish his round, but Foster couldn't manage a birdie on his final two holes and the Frenchman emerged with his sixth European Tour win and first since 2009.
Levet ended the day at 7-under 285, one better than Olesen (70) and Foster (74), who failed to card a birdie Sunday.
Grabbing fourth place was Martin Kaymer, who shot 2-over 73 to end at 4-under 280. Simon Khan (71) and Richie Ramsay (76) knotted in fifth at minus-3.
Third round co-leader James Morrison stumbled to a 7-over 78, falling into a share of seventh place.