Tunisian Jabeur, who is ranked 204th in the world, came through to win 6-2 7-5 in one hour and 24 minutes to knock the number one seed and world number 37 out.
There was no such shock for fourth seed Alexandra Cadantu, although she was pushed all the way in a match which lasted two hours against Mandy Minella. Romania's Cadantu dropped the first set before winning 5-7 6-1 6-3.
Second seed Donna Vekic booked her place in the next round with a 6-1 6-2 win over Tetyana Arefyeva while third seed Chanelle Scheepers won her opening match, beating Andrea Hlavackova 3-6 6-3 6-4.
In the other games, Galina Voskoboeva, Elina Svitolina and Kateryna Kozlova all came through their first-round matches.