As against Sofia Kenin on Monday and Peyton Stearns on Tuesday, Tauson was not necessarily exuberant but very focused and strong in serving.
On Wednesday, she did not deliver the same large number of aces as in the previous matches, but on the other hand, Tauson won a very large portion of her first serves against a slightly confused Linette at times.
The 34-year-old Pole is ranked 50th in the world and on Tuesday surprisingly knocked out the eighth-seeded Russian Ekaterina Aleksandrova in Dubai, but against Tauson, she never settled into her stride.
In the first set, Linette was not really close to breaking the 11-year-old younger Dane, and when Tauson took advantage of her break point to make it 5-4, the set was decided.
Tauson opened the second set with another service breakthrough and steered safely towards victory when she also broke to make it 4-1.
Linette bounced back and created some excitement with her first break of the match to make it 4-2, but Tauson then stepped up a gear and took control of the match again with heavy returns and serving home the tie in comfortable fashion.
Tauson will face American opposition in her quarterfinal. It will be either 18-year-old Iva Jovic or fourth seed Jessica Pegula.