The Dane also won the title in 2002 for his only previous European Tour victory. Rose had a chance to extend the playoff, but missed his birdie attempt from 20 feet.
Hansen shot 69 and Rose 71 in persistent rain at Wentworth to finish on 8-under 280, a stroke ahead of Vijay Singh and Richard Sterne. Singh shot the day's best score of 66 and Sterne had a 74.
Overnight leaders Paul Broadhurst and Ross Fisher faltered in the final round. Broadhurst (80) had two sevens on his card and he finished tied for 20th. Fisher (84) began with five bogeys and finished tied for 39th.