
The German, a former world number two who has been plagued by injuries, dug deep to save three set points in the second set tiebreak and despite a third set recovery by the Serbian, Haas stayed on course to become the oldest champion since Arthur Ashe in 1975.
"I am playing some of my best tennis. I didn't have too many expectations coming here but the win at Halle was great for my confidence," said Haas who was two sets ahead against Federer in the French Open last month before the Swiss hit back.
Roddick, seeded sixth, was on course for the last four when he broke in the fourth set against Hewitt after taking a two sets to one lead, but the Australian defied a leg injury to send the match to a final set.
The American last reached the semi-finals at the All England Club in 2005 when he went on to suffer the second of two successive final defeats to Federer.
"It's my second Grand Slam semi-final of the year having not figured in the picture for a while," said Roddick.