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World No 2 Clijsters, who won in 2005 and 2003, swept past Russian Alla Kudryavtseva with a dominating 6-2, 6-0 victory in the second round of the WTA and ATP Masters 1000 tournament.
Jankovic also showed plenty of firepower, crushing Coco Vandeweghe of the United States in straight sets 6-2, 6-1.
Serbia's Ana Ivanovic, who won here three years ago, was scheduled to take to the court later as part of Friday's evening session.
The women's draw also includes world No 1 Caroline Wozniacki of Denmark who lost in the final last year to Jankovic 6-2, 6-4.
Second seed Clijsters needed just 52 minutes to beat Kudryavtseva and advance to play Sara Errani. Italy's Errani defeated Jarmila Groth 7-5, 4-6, 6-2.
Belgium's Clijsters clinched her match when the Russian's forehand return sailed wide left.
"I was happy to be playing out on centre court," Clijsters said. "For a first match, I'm at a stage now where I haven't played for a while, and when I was playing, my last few tournaments were indoors.
"So I kind of just have to get back into playing outdoors again and big arenas, and just get a feel for it all over again."
Clijsters could surpass Wozniacki with a strong performance in Indian Wells. Clijsters was ranked 133rd in the world when she won in 2005.
She hit three aces, won six of nine break-point chances and won 65 percent of the total points against Kudryavtseva. Clijsters won the second set in a blistering 21 minutes.
Jankovic began her title defence in equally dominating fashion, hitting four aces and winning 80 percent (20 of 25) first-serve points.
She is trying to become the first woman since Martina Navratilova in 1990-91 to win back-to-back Indian Wells titles.
"The last couple of weeks I have been starting to feel confident in my game," Jankovic said.
"She made a lot of mistakes. I didn't really know what to expect because I only played her once before at the US Open. But I knew she had a big serve."
Jankovic moves on to the third round where she will play Julia Goerges of Germany who beat Austrian Sybille Bammer 6-1, 6-3 on Friday.
In other key women's matches, reigning French Open champion Francesca Schiavone of Italy dominated Czech Zuzana Ondraskova 6-2, 6-0 and 12th seeded Petra Kvitova lost 3-6, 6-2, 7-5 to fellow Czech Barbora Zahlavova Strycova.
Wozniacki, two-time Indian Wells champ Daniela Hantuchova and former world No. 1 Maria Sharapova of Russia play their first matches on Saturday.
In the men's draw, Milos Raonic of Canada hammered 10 aces and used his thundering forehand to overpower Turkey's Marsel Ilhan 6-2, 7-6 (7/4) in his opening match.
"I feel good. I feel like I played a lot better today," Raonic said. "My goal is to keep getting better and improving."
Raonic unleashed a 148-mph (238-kmh) ace in the second game of the second set against Ilhan in front of a crowd of 5,000 on an outer court.
He also had 140-mph and 138-mph serves in the final game of the first set but said he wasn't entirely happy with the way he was serving Friday.
"I didn't feel like I served all that well today," he said. "I have been working on improving my second serve."
Raonic hit one second serve early in the match that kicked up so high Ilhan had to use an overhead smash to get it back.
Raonic advances to the second round, where he will face American Mardy Fish, whom Raonic beat last month in the ATP Memphis semi-finals before going on to lose to Andy Roddick in the final.
"I look forward to it," Raonic said of meeting Fish again. "I feel like I am playing well from the back. If I keep this up good things will come."
In other men's matches, Igor Andreev of Russia defeated Japan's Kei Nishikori 6-4, 6-7 (2/7), 6-4, Australia's Bernard Tomic outlasted Rohan Bopannna 6-7 (5/7), 7-6 (7/1), 6-3 and Benjamin Becker of Germany ousted Thiemo De Bakker 6-2, 7-5.
The men's draw heats up Saturday with world No. 1 Rafael Nadal of Spain facing South Africa's Rick De Voest and defending champion Ivan Ljubicic of Croatia taking on Argentina Juan Martin del Potro in a second round contest.
