The British number two and her Kiwi opponent battled for nearly three hours before the match was decided on the 20th point of a third-set tie-breaker.
Erakovic dominated the first set but Keothavong managed to fight back in the second and force a decider.
Her campaign was ended though as Erakovic edged the tie-break to move into the second round, where she will now play South African Chanelle Scheepers.
Another Brit Emily Webley-Smith was also bounced out of the competition at the first time of asking, the nation's number six losing 6-1 6-2 to Croatia's Mirjana Lucic .
Second seed Jankovic dropped the opening set on a tie-break in her match with Yaroslava Shvedova but recovered to claim the second - also on a tie-break - before romping home in the third.
The Serb's 6-7(7) 7-6(4) 6-1 victory sets up a second-round meeting with Dutchwoman Arantxa Rus.
The Chinese will now meet Pauline Parmentier, who beat Irina Falconi 6-1 6-4 to progress, while Australian Casey Dellacqua secured her place in the second round with a 6-2 6-2 win over Irina Begu of Romania.
Meanwhile, young Canadian Eugenie Bouchard impressed again in a 6-4 6-3 victory over Galina Voskoboeva of Kazakhstan.