The Belgian will now meet Vera Zvonareva in the last four in a rematch of last year's US Open final, which Clijsters won.
She was not at her best today but her experience counted at key times as she came through 6-3 7-6 (7/4).
The match started wildly with three successive breaks of serve with Clijsters claiming two of the them.
She broke again for a 4-1 lead and, although Radwanska claimed one of them back, the Pole then conceded her serve once more to hand Clijsters the set.
The third seed also made the first move in the second set by moving 4-2 ahead only to squander her advantage as her concentration wavered.
Radwanska countered by winning three games on the trot to set up the chance to serve for the set but she could not see it out as it went to a breaker, in which Clijsters always had the upper hand.
Despite the win, Clijsters was not entirely happy with her performance.
She said: "I didn't feel great out there today. I felt heavy in the legs but I hung in there which I needed to because she is a good player."
And Clijsters admitted she will have to improve when she meets Zvonareva, adding: "I hope my experience can help me but there are some tough players out there. It's going to be tough but they will be two great semis. I lost to Vera at Wimbledon last year but then beat her at the US Open. She is playing really well and I am going to have to play better than I did today."