The match started later than expected, as play had been interrupted earlier in the day due to the heat in the Chinese city. Therefore, it suited Tauson just fine to get through the hardships in just two sets.
The match began somewhat unrhythmically with unstable play from both players, but the Dane was the first one to gain control of her game.
After a couple of Serbian errors, Tauson capitalized on her third break point of the match to break for 2-1. In the following game, the Serbian had two chances to break back, but Tauson held on.
In the subsequent service games, the Dane had good control of her serve, and another break gave her the first set with a hard forehand winner on the first set point.
In the first game of the second set, Tauson faced three break points, but Tauson came up with three successive aces to avert the danger.
Instead, Tauson went up 3-1, but Danilovic answered back to tie the game at 3-3.
Ahead at 5-4, Tauson squandered a match point in Danilovic's serve, but the Dane got another chance at 6-5, and this time she broke to win when the Serbian made an unforced error with her backhand.
In the second round, Tauson will face either Magda Linette from Poland or the Croatian Antonia Ruzic.