Clijsters, who has been nursing a right shoulder injury since she won the Australian Open in January, had eight double-faults Wednesday night and held only three times in nine service games.
"I just didn't feel good out there," Clijsters said. "I didn't have any fighting spirit. Against some lower-ranked players maybe it's possible to get through matches, but against somebody like her, it's not."
Azarenka, seeded eighth, earned the biggest victory of her career when she won Key Biscayne in 2009. Her opponent Thursday will be No. 3-seeded Vera Zvonareva, who beat No. 9 Agnieszka Radwanska 7-5, 6-3.
Zvonareva overcame a set point with an ace in the first set and won four consecutive games to take control of the second set.
Zvonareva improved to 4-0 in quarterfinals this year.
"I'm definitely more experienced and I'm more mature," she said. "I'm just trying to enjoy my time on the court. I don't really think about anything else when I'm out there."
Zvonareva's best showing in 10 appearances at Key Biscayne was in 2008, when she lost in the semifinals.
Information from The Associated Press was used in this report.