Vying for her maiden Australian Open Singles title, she lost her serve twice in the first set. But she came back brilliantly to beat Agnieszka four times to clinch the opening set.
Clijsters, came into the match with an injured leg and said, "I felt heavy in the legs - I felt tired out there but I just hung in there."
Kim Clijsters had an high error rate in the match, but the defensive approach taken by Agnieszka ensured that it didn't her too much.
She is the reigning US open champion and is a firm favourite for the Women's singles title. For a berth in the final she now has to go through the second-seeded Vera Zvonareva in the semi-final.