The 23-year-old top seed, who won her first major tournament in Melbourne last year, burst into tears after she successfully defended her claim to the Daphne Akhurst Memorial Cup, becoming one of only eight women, including Steffi Graf, Martina Hingis and Serena Williams, who have done so.
Eighth seed Golovin beat fellow 19-year-old and sixth seed Ivanovic of Serbia 6-4 3-6 6-4 in the first of the semi-finals on the green clay.
The 16-year-old eighth seed looked in good form as she earned a hard fought 6-3 7-6 (7-3) victory.
The Italian faces Romania's Monica Niculescu next after the 23-year-old beat 32nd seed Tsvetana Pironkova of Bulgaria 6-4 6-1.
The 31-year-old beat third seed Nadal for the second time in seven meetings, with his other victory back in 2005.
It was the first time the 19-year-old had beaten 18th seed Zheng in four meetings, and also gave her a first semifinal berth at Indian Wells.
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The 17-year-old from Bolton ousted the 15th seed from Ecuador in two hours and 19 minutes.
The 25-year-old Djokovic will play Ukrainian 14th seed Alexander Dolgopolov, who dispatched Stanislas Wawrinka of Switzerland in straight sets.
The 27-year-old beat former champion and seven seed Jankovic despite letting slip a 5-2 lead in the first set, Martinez Sanchez eventually fighting back to win via a tie-break.
The 20-year-old Mathieu started badly against the seventh seed, losing his serve in the opening game of the match.
Then Harriet's Mercantile, which sells Granny Opal's Blueberry Muffin Mix (Granny Opal being Mr. Gettle's 78-year-old grandmother) and which has a seed museum upstairs.
The 20-year-old will face either Marcos Baghdatis or second seed Rafael Nadal in the third round.
The Serbian ninth seed cruised past 19-year-old world No. 114 Eugenie Bouchard of Canada 6-2 6-1 for the 500th victory of her career.
She will next play 17-year-old Kristyna Pliskova after the Czech knocked out top seed Timea Babos.
The 20-year-old showed her grit to move past Russian seventh seed Safina after falling a break behind in every set.
The other semifinal will be between 2006 Australian Open finalist Marcos Baghdatis of Cyprus and 21-year-old Bulgarian Grigor Dimitrov, who upset Austrian seventh seed Jurgen Melzer.
Third seed Victoria Azarenka will face 19-year-old German Annika Beck in the next round following a routine win over Elena Vesnina.
Sock had the seeming tough luck of drawing 22nd seed Florian Mayer, a wily 28-year old veteran who had made it to the Wimbledon quarterfinals.
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The 19-year-old had earlier kept her nerve to see off eighth seed Svetlana Kuznetsova in a hard-fought three-setter lasting two hours 40 minutes in blazing temperatures.
The 28-year-old former world number one will face Egypt's fifth seed Amr Shabana in the last four.
The 18-year-old Krajinovic, a wildcard entry, will play American third seed Sam Querrey for a place in the Belgrade final.
In the first-round match between Martina Hingis and Jelena Dokic, the number one ladies' seed was knocked out by the 16-year-old and the score was an extraordinary 6-2, 6-0.
The 30-year-old produced a massive shock, knocking out local favorite and 24th seed Julia Georges in a 7-6 (10-8) 6-0 victory.
His fellow American Sam Querrey lost to Australia's 19-year-old rising star Bernard Tomic , who will next face Ukrainian 13th seed Alexandr Dolgopolov.
He will next face 31-year-old French qualifier Sebastien De Chaunac, who later upset No. 14 seed Dmitry Tursunov of Russia 3-6 7-6 (7-3) 7-5.
The 17-year-old beat his teenage counterpart to book a second-round meeting with sixth seed Fernando Gonzalez.
However, 28-year-old Gonzalez, who had overpowered all his previous Roland Garros opponents including third seed Andy Murray, began to fight back.
Clijsters, the 14th seed but champion in Miami in 2005, crushed 20-year-old Czech Petra Kvitova 6-1 6-1 to earn a third-round clash with Israel's Shahar Peer.
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Alize Cornet ended the hopes of 19-year-old American Lauren Davis, who was allowed into the main draw when second seed Victoria Azarenka pulled out due to ongoing ankle problems.
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