Former world No.1 Swiatek powered on at SW19 as she won 6-4 6-1.
Swiatek next faces world No. 19 Liudmila Samsonova for a spot in the semi-finals.
“Even though the beginning was pretty shaky, I managed to play well and solid,” said Swiatek, who hit four double faults in her first two service games.
“I am not sure if Clara felt well, she said at the net she was sick, so hopefully she will have a good recovery.
“This year for sure I feel like I can play my game and hopefully it will last as long as possible and I will just keep working.”
Of the three surfaces that the tennis majors are played on, grass has been Swiatek’s least successful by a distance.
However, after making her first final on the surface in Bad Homburg last month, she has impressed at Wimbledon.
Andy Roddick said after the third round that Swiatek “looks way more comfortable on grass this year” – and that looked the case again against Tauson.
The Dane had beaten big-serving Elena Rybakina in the previous round and started strongly with two breaks in the first three games, helped by four double faults from Swiatek.
But Swiatek hit back to level at 3-3 and then broke again to win the set.
Swiatek carried the momentum into the second set, reeling off five games in a row from 1-1 to seal victory.
Swiatek has won all four previous meetings against Samsonova, but this will be their first on grass.
“She is a really solid player,” Swiatek said about Samsonova.
“She is an even (player) from both sides. We’ve played many matches. We have played three-setters as well and I remember it wasn’t easy. I know that she can play well on fast surfaces so I will prepare tactically because I haven’t been watching any matches and I will trust what my coach says. I will be ready.”
