The 22-year-old Dane secured the first victory of her career at Wimbledon by beating Britain's Heather Watson, who is ranked 143 in the world.
23rd-seeded Tauson played a miserable first set, but without putting on a flashing performance, she fought back to win 2-6, 6-4, 6-3.
So, at least one Dane is still involved, when the second round is played from Wednesday. On Monday, both Holger Rune and Elmer Moller went out in the first round, with August Holmgren having to play later Tuesday afternoon.
Tauson recovered some of her best tennis in the third set, and after being behind 2-3, she won the last four games of the match.
In the last two sets, the Dane managed to get her serve going, which was missing in the first set, where she was broken three times.
Watson often punished Tauson's passivity in the first set with her accurate backhand, and she caught Tauson with drop shots as the Dane tended to stay too far back.
Tauson otherwise got off to a good start, when she took advantage of several weak serves from Watson to lead 2-1, but from there on, Watson took control.
The Dane took virtually no initiative in the duels and neither her strong forehand nor her serve worked to her advantage.
After just over half an hour of tennis, Watson had turned a 1-2 deficit into winning the first set 6-2 .
Tauson improved from the start of the second set, where she took advantage of a couple of British errors to break to 1-0.
At the same time, the Dane improved her serve, and as she did not give away a single break ball in the entire set, she was able to serve the set home to restore parity in the match.
In the third set, the players were tied at 3-3. Both had their chances, but Tauson was the first to break serve at 4-3, flashing her forehand.
The 33-year-old Watson then crumbled, and Tauson closed out the match with a clean break to make it 6-3.
