The tenacious Italian beat Arantxa Rus of the Netherlands 6-1, 6-2 Sunday in the opening match on Court Suzanne Lenglen.
Errani reached a Grand Slam final for the first time a year ago at Roland Garros, then lost to Maria Sharapova.
Now ranked a career-best No. 5, Errani dominated Rus from the baseline, won four games at love and advanced in 54 minutes. Rus, ranked 86th, double-faulted seven times and lost her 13th consecutive match on the WTA Tour.
Past champion Ana Ivanovic of Serbia overcame an inconsistent performance in a chilly start at the French Open and held on to beat 108th-ranked Petra Martic of Croatia 6-1, 3-6, 6-3 Sunday.
The 14th-seeded Ivanovic, who won the title at Roland Garros in 2008, began the first-round match well while wearing a long-sleeved shirt with the temperature dipping to 55 degrees.
But Ivanovic faltered in the second set, then had trouble closing out Martic before finally converting her fifth match point.
Martic showed she can be tough on red clay by knocking out eighth-seeded Marion Bartoli en route to reaching the fourth round at Roland Garros last year.
Serena Williams and Roger Federer were among others on the first day's schedule. Play began under cloudy skies with the temperature in the mid-50s.
French Open: Sara Errani, Ana Ivanovic advance to second round
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