Halep served for the match while leading 5-4 in the third set, and she came within two points of victory. But Jankovic broke her there, and took the final three games.
Jankovic was the 2008 runner-up at Flushing Meadows and has a chance to overtake Serena Williams at No. 1 in the rankings by winning the tournament this year. The 96th-ranked Halep, meanwhile, never has won a match at any major tournament. She lost in the first round at the French Open in her Grand Slam debut.