Jankovic defeated Muguruza 6-3, 6-0 shortly before showers interrupted the first matches of the day on 12 other courts.
Zheng Jie also reached the third round, beating Melanie Oudin of the United States 6-3, 6-1.
With the midday temperature in the mid-50s, Jankovic took the court wearing pink leggings and a long-sleeve pink shirt. She beat Muguruza with steady play from the baseline while the 19-year-old Spaniard committed 29 unforced errors.
Jankovic, seeded 18th, is a three-time semifinalist at Roland Garros.
On the men's side, No. 16 Philipp Kohlschreiber advanced when Yen-hsun Lu withdrew because of a right ankle injury.
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