German 22nd seed Julia Gorges also progressed along with Romania's No. 31 Monica Niculescu and Czech No. 32 Petra Cetkovska.

CNN: No. 1 Wozniacki wins Melbourne opener

Second seed Julia Gorges of Germany also advanced, again in three sets, as she saw off Garbine Muguruza of Spain 7-5 5-7 6-2.

CNN: STORY HIGHLIGHTS

Kanepi won 6-1 4-6 6-0 against the 21-year-old conqueror of Germany's No. 25 Julia Gorges to match her 2008 effort of reaching the quarters.

CNN: June 4, 2012 -- Updated 1944 GMT (0344 HKT)

The 22-year-old will climb to a career-high No. 5 after winning the Dubai Tennis Championships on Saturday, when she beat Germany's rising star Julia Gorges 7-5 6-4 in the final.

CNN: Radwanska reaches new heights with Dubai success

The top two seeds remain on track for a final showdown after both Azarenka and three-time grand slam champion Maria Sharapova won, against Germany's Julia Gorges and Italian Roberta Vinci respectively.

CNN: STORY HIGHLIGHTS

Polish eighth seed Agnieszka Radwanska beat Kazakhstan's world No. 57 Galina Voskoboeva 6-2 6-2 to set up a clash with Germany's rising star Julia Gorges , who is in the fourth round of a grand slam for the first time.

CNN: Clijsters faces Li in Aussie final rematch