The Polish second seed was pushed to the limit in the first set on Rod Laver Arena before prevailing 7-6 (7/5), 6-3 after more than two hours to set up a clash next with Czech player Marie Bouzkova.

Victory was a welcome boost for Swiatek, who lost her last two singles matches at the lead-up United Cup -- to Coco Gauff and Belinda Bencic.

But 35 unforced errors will be a worry against a player who had only made it past the first round once in 13 previous Grand Slam appearances.

"I was a bit rusty at the beginning, I didn't really start well and she used the opportunity," she said.

"But I knew if I could put the hard work in, I would play better. So that's what I tried to do from the middle of the first set.

"I'm happy that it worked. For sure, many ups and downs, I have some stuff to work on, so I'll just focus on that."

Swiatek has won four French Opens, the US Open and Wimbledon, but a title at Melbourne Park has proved elusive.

The 24-year-old has made the semi-finals twice but never gone further.

Should she finally win the title and complete the career Grand Slam she would be only the seventh woman in the Open era to do so and the third youngest after Steffi Graf and Serena Williams.

Yuan, ranked 130, was unfazed by facing a player of her stature and came out with all guns blazing.

She broke a shaky Swiatek's first service game and consolidated with a hold.

Swiatek had to fend off a break point on her next serve before she settled and got on the board.

With her radar seemingly starting to function, she broke to level the set at 3-3, but Yuan again pounced to break back.

Swiatek finally came good when Yuan served for the set, with her powerful groundstrokes too much for the Chinese player.

It headed for a tiebreak where Swiatek again had to fight hard before getting over the line, with 21 unforced errors in the set.

She raced 3-0 clear in the second set and when Yuan had a medical timeout for a lower back issue, it appeared to be all over.

But the plucky 27-year-old won the next two games to stay alive before running out of steam.