Clijsters dropped just three games in her opening two matches but the Belgian player struggled against Azarenka, who reeled off four games in a row to close out the match.
"I felt I was looking for rhythm and timing, compared to my singles yesterday," Clijsters said. "Her shots are hard and low, and it's tough to get an angle against her."
Story continues below ↓advertisement | your ad hereThird-seeded Samantha Stosur beat Britain's Elena Baltacha 6-7 (5), 6-1, 6-0 to reach her fifth semifinal of the year and eighth-seeded Marion Bartoli of France edged Maria Jose Martinez Sanchez of Spain 5-7, 6-4, 7-6 (5).
Svetlana Kuznetsova's miserable year continued when she was defeated 6-4, 7-5 by qualifier Ekaterina Makarova in an all-Russian clash.
The unseeded Azarenka earned her first break with a winning forehand down the line to take a 3-2 lead before Clijsters saved six set points to level at 5-5.
Azarenka, who this week earned her first back-to-back victories in six tournaments, took the set in the tiebreak on her ninth set point and then recovered an early break in the second.
Up 2-4, Clijsters suddenly lost her way and netted a forehand volley on match point to hand Azarenka victory.
"I was up 4-2 and it went quickly from there - a couple of double faults and good returns from her which pushed me back," Clijsters said. "I wasnt able to dictate and felt I was being pushed back a bit."
French Open finalist Stosur struggled early on and netted a backhand volley to hand Baltacha the first set in the tiebreak.
But the Australian player, who also made the Eastbourne semifinals in 2008, was more aggressive in the second set as she hit 18 winners and allowed Baltacha just six points in the opening four games.
The early games of the third set were closely contested but Stosur pulled clear and closed out her final service game with three aces.
Kuznetsova, the 2004 champion who has slipped to No. 20, was taken to three sets in her first two matches but could not get past Makarova, who had reached the quarterfinals for the third year running.
Bartoli needed two hours, 51 minutes to reach the last four of the Wimbledon warmup tournament for the fourth straight year.
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