The Barcelona-based eighth seed, a former French Open quarter-finalist, edged a tight first set and completed his victory when Ancic netted a volley on match point.
The towering 22-year-old Croat looked short on energy, having battled back from a set down to win his last three Hamburg matches while Robredo had only dropped one set all week.
Earlier, 15th seed Stepanek profited from an excellent start to defeat Argentina's Jose Acasuso 6-4, 7-6.
With the umbrella-like retractable roof over centre court closed to keep out the rain showers, the Czech broke the unseeded Argentine in the first game of the match.
That was enough to secure the first set and he sealed the second set tie-break 7-5 on his first match point when Acasuso netted a forehand.
Related News: v Ancic, Robredo into Hamburg Semis 2006-05-20
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