Erakovic had a nervous start, going down in just 37 minutes to the third seeded Jankovic with a stilted display.
The 20-year-old New Zealander's plan to try and build an opening for a point did not work with Jankovic ending rallies with winners at the first opportunity.
After taking four games to work Erakovic out, Jankovic made the first break in the sixth game while leading 3-2.
Erakovic was broken to love, giving her opponent the opening she needed.
Jankovic held serve in the next game after Erakovic battled hard to get to 30-30. But the New Zealander made two loose returns to allow Jankovic to consolidate her break.
Erakovic was unable to close out the eighth game despite twice holding game point and Jankovic won on her fourth set point.
Erakovic was also punished for her unforced errors but raised her game in the second set to give her opponent a run for her money.
Jankovic called for a trainer with the score at 3-2 as the set went with serve, complaining of a sore right forearm.
Erakovic made Jankovic work hard in the fifth game and was unlucky not to have finished off a couple of well-created openings which could have given her the game.
But Jankovic, although troubled by a weak forearm, managed to break Erakovic in the next game to take a 4-2 lead.
Erakovic, showing an ability to vary her game and mix her play up broke back immediately.
Erakovic took a 6-5 lead with a break in the 11th game but Jankovic, winner of six WTA singles titles, broke back immediately to tie 6-6 and send the match into a tie break.
Erakovic went into a 5-3 lead in the tie break but Jankovic pulled herself together to score four points in a row to take out the match.
Erakovic made 12 winners in the match compared to Jankovic's four -- the difference coming from her 31 unforced errors to Jankovic's 19.
The 60 ranking points earned will see Erakovic close in on the world's top 70 at the end of Roland Garros.
She's also guaranteed to take home 23,760 euros ($NZ47,000) for reaching the second round.
