The 78th Tunisian woman in the world has won two games, as opposed to Danish, one of the best tennis players in the world.
Runs came in 7-5, 3-6, 7-5 in a match that lasted for 130 minutes.
Anas said on her Facebook account: “I am very happy to have reached the fourth round of the Grand Slam tournament for the first time in my career.”
“I congratulate Caroline on her amazing career, you were an example of inspiration, and I am fortunate to be playing with you.”
In the fourth round of the championship, Anas will meet Chinese Wang Qiang, ranked 29th in the world.
Ranked 78 in the world, she defeated the first round in the British world, Joanna Conta, ranked 12th in the world, with two sets, without charge.
Rimontada then beat Frenchman Caroline Garcia, ranked 46th in the world and second in the past, after losing the first group 6-1 but returned strongly to win the second and third sets 2-6 and 3-6.
The most prominent achievement of Tunisian participation in the Grand Slam tournaments was to reach the third round of the American Open 2019 and Roland Garros 2017.
Anas Jaber won the Roland Garros Junior Women Championship in 2011 as the first North African player.