Tauson is through to the second round of the French Open after a three-set victory over Polish outsider Linette.
Tauson, seeded 22nd in the Grand Slam tournament, was already tired of drawing the highest-ranked player of all unseeded players going into the match, but the Dane still managed to progress winning 6-4, 4-6, 6-1.
Leading 4-2 in the second set, Tauson seemed to be on her way to a certain victory in two sets, but Linette produced a stunning comeback to force the match into a third set. In the third set, however, there was no doubt about the result.
The 22-year-old Dane played a good match at times, but there is also room for improvement, and the level was uneven as she delivered big winners but also had a high percentage of unforced errors.
It was an uneven first set, where the Dane found it difficult to maintain momentum, when she was on top but when she broke Linette's serve to lead 5-4 she finally sustained her high level in her own serve to secure the first set.
Tauson continued her bright from the beginning of the second set and despite Linette adding more stability to her game, Tauson managed to take a 4-2 lead and looked headed for a comfortable win.
But then Linette rediscovered her highest level and won successive games to level the score.
Tauson began the third set with a different attitude and immediately broke Linette's serve with a heavy forehand winner.
This time there was no response from Linette, and Tauson dictated play from the baseline with forceful strokes to take a reassuring 4-0 lead.
The Dane closed the match after a little more than two hours, when she broke Linette's serve clean.
In the second round Tauson will face the Dutch contender Arantxa Rus (No 94 in the world) on Wednesday, who on Monday delivered a minor surprise by beating Colombian Camila Osorio, No 54 in the world.