Clijsters raced through the first set 6-1 only to see the Serb win nine of the next 10 games as she won the second set 6-1 and then built a 3-0 lead in the decider.
But the Belgian, playing her first match on tour since August, saved a break point in the fourth game of the decider and then ran off with six games on the trot to complete the 6-1, 1-6, 6-3 win.
Clisjters could next meet top seed Sam Stosur who plays her second round match on Wednesday.
Also advancing into the quarterfinals were second seed Andrea Petkovic, who beat Czech Barbora Zahlavova Strycova 7-6, 6-0 and third seed Francesca Schiavone, a 6-4, 6-4 winner over Galina Voskoboeva.
Slovakia’s Daniela Hantuchova also booked a last eight berth with her second consecutive three set win at this event. Hantuchova came from a set down to beat American qualifier Vania King 4-6, 6-2, 6-3.
Stosur and Serena Williams will be in action on Wednesday as they aim to advance to the quarterfinals.
BRISBANE INTERNATIONALBrisbane, Australia
Tuesday, January 3, 2012 – Singles – Second Round(2) Andrea Petkovic (GER) d. Barbora Zahlavova Strycova (CZE) 76(2) 60(3) Francesca Schiavone (ITA) d. Galina Voskoboeva (KAZ) 64 64(5) Kim Clijsters (BEL) d. Ana Ivanovic (SRB) 61 16 63Daniela Hantuchova (SVK) d. (Q) Vania King (USA) 46 62 63
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