There was little to separate the two players during the early exchanges, with both trading breaks in the opening two games. McHale looked to have made the breakthrough when she broke the 10th seed to move 4-2 ahead.
However, Jankovic recovered with two breaks of her own before serving out the set 6-4.
The Serbian made a strong start to the second set, breaking McHale twice to race into a 3-0 lead. McHale responded with a break of her own, but Jankovic powered through to take the set 6-4.
Jankovic will now face Coco Vandeweghe in the second round.