Jankovic served seven aces in knocking out "lucky loser'' Czink, who lost in the second round of qualifying but got into the main draw when Svetlana Kuznetsova withdrew with an injured right knee.
Czink's tournament run included a 6-3, 6-3 upset of 13th-seeded Virginie Razzano. The 25-year-old Hungarian reached the third round of a WTA event for just the second time this year.
Jankovic can dislodge countrywoman Ana Ivanovic from the top ranking by winning the tournament, her first since injuring her right knee at Wimbledon.
"There's no pain and I'm really happy about that,'' she said. "My legs are a little bit hurting. I'm not used to playing matches every day and playing after not doing anything for two weeks. Now it's time to get in shape.''
Jankovic is wearing tape on her knee for protection.
"Without the tape, it would be a risk because the knee is still fragile,'' she said.
Jankovic served seven aces - never her strong suit - with her serve bailing her out at love-40, 2-all to win that game. She connected on just 28 percent of her first serves Wednesday, but improved to 63 percent Thursday, when she won 81 percent of her first-serve points.
"If I could hit this serve every day like that, my life would be so much easier,'' she said, laughing. "You don't have to break a sweat and you're winning games.''
Jankovic wore a hot pink dress, which was late arriving. She wore a white top and skirt, which didn't fit well, a day earlier.
"The pink dress played better today,'' she said.
Third-seeded Anna Chakvetadze of Russia couldn't say the same. She was upset by 14th-seeded Sybille Bammer, 6-4, 5-7, 6-2. Also dismissed was No. 5 Vera Zvonareva, who lost 6-4, 7-5 to Nadia Petrova, last year's runner-up.
Petrova will play Jankovic in Friday's quarterfinals.
No. 4 Dinara Safina fought off a match point in outlasting Russian countrywoman Alla Kudryavtseva, 7-6 (1), 0-6, 7-6 (3) in a late match.
Other winners were No. 8 Victoria Azarenka of Belarus, No. 10 Flavia Pennetta of Italy, and Yuan Meng of China.
While Czink's run ended, Bethanie Mattek kept rolling.
The 23-year-old player from Miami defeated Olga Govortsova of Bulgaria, 7-5, 6-2, to continue a solid showing that began in April. She trailed 5-2 in the first set.
"I was just making a couple mistakes and she was playing well,'' Mattek said. "I got a little more intense and rattled off seven games in a row.''
Mattek has boosted her ranking nearly 100 places since then and can expect to rise higher, helped by her upset of 11th-seeded Nicole Vaidisova earlier this week.
"I've been playing really well. It just keeps building every match I play,'' she said. "If I do play up to my potential, I'm expecting myself to win. I'm really confident in my game right now. Two years ago, I couldn't say that.''
Kuznetsova and 10 other players, including Wimbledon champion Venus Williams, Serena Williams and Lindsay Davenport, withdrew from the $650,000 tournament.
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