The 21-year-old third seed, a finalist at the Australian Open and semi-finalist at Wimbledon already this season in his breakthrough year, won a tight first set with a beautiful passing shot and raced through the second at a canter.
Fourth seed Ancic, who returned this week after two months out with an injured knee, made too many errors to threaten the athletic Baghdatis despite his impressive serve.
Baghdatis, the world number nine, claimed his first victory over Ancic in four attempts when the Croatian went long with a forehand after an hour and nine minutes.
