The former world No. 1 took 2 hours, 20 minutes to down the 18-year-old Halep amid stifling heat at the USTA Billie Jean King National Tennis Center, where on-court temperatures soared past 100 degrees.
Jankovic, who finished second at the 2008 tourney to American great Serena Williams, advanced to face Croat Mirjana Lucic in the second round.
Meanwhile, former U.S. Open winner Svetlana Kuznetsova of Russia, the 11th seed, defeated 39-year-old Kimiko Date Krumm of Japan, 6-2, 4-6, 6-1, winning in just under 2 hours on the Grandstand Court.
Eighth-seeded Chinese Li Na was a victim of an upset at the hands of Ukrainian Kateryna Bondarenko, losing 2-6, 6-4, 6-2, and ninth-seeded Pole Agnieszka Radwanska breezed past Spaniard Arantxa Parra Santonja 6-4, 6-3.
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