0742 GMT January 23, 2019
The Pole disposed of Romania's Sorana Cirstea 6-0, 6-3 in an hour and 18 minutes. Cirstea, ranked 78th in the world, lost more than half the points she served and faced 14 break points, losing six of them, AFP reported.
It was a contrast to the defending champion's first-round match on Monday, when she took nearly two and a half hours to overcome a stiff challenge from a 103rd-ranked Chinese opponent.
Britain's Johanna Konta, who has begun 2017 as a top 10 player for the first time in her career, had a scare of her own against 77th-ranked Vania King of the US on Tuesday, losing the first set 1-6.
Konta recovered to prevail 1-6, 6-3, 6-2 in an hour and 35 minutes to reach the quarterfinals of the Shenzhen Open in China.
Konta, who is the third seed at the event, will face either Kristyna Pliskova or qualifier Kai-Chen Chang in the last eight.
But unseeded home player Wang Qiang caused an upset, putting out seventh seed Monica Niculescu of Romania 7-6 (7/1), 6-4, in a grueling encounter that lasted more than two hours even though the pair only played two sets.
In the day's other singles match at the $750,000 tournament in the southern Chinese city of Shenzhen, American eighth seed Alison Riske beat Bulgaria's Tsvetana Pironkova 6-1, 6-1.
French Open champion Garbine Muguruza saved a match point before seeing off Russia's Daria Kasatkina in the second round of the Brisbane International on Tuesday.
The 23-year-old Spaniard won 7-5, 3-6, 7-6 (9/7) over the 19-year-old Kasatkina, who served for the match at 5-4 in the third set, only to be broken by the fourth-seeded Muguruza.
Muguruza then kept her nerve in the tiebreak, holding on to win in just under three hours.
It was her second three-set win in as many days after she edged Australian Samantha Stosur on Monday.
"Obviously I'm tired," Muguruza said. "I would prefer to play a one-hour match and to be super good. But I think those tough matches are going to help me to win confidence.
"It's very helpful. I mean, to start the year playing these kind of matches gives me, I don't know, a good feeling.
"I think it was a battle, literally," she added.
"I think we both played very good during the whole match. We could see in the tiebreak there is, like, nobody knew who was going to win the match until the end."
Third seed Czech Karolina Pliskova earlier continued her impressive form when she stormed past US qualifier Asia Muhammad 6-1, 6-4.
However, sixth seed Elina Svitolina was pushed hard by American Shelby Rogers before winning in three sets 7-5, 2-6, 7-5.
France's Alize Cornet stormed into the quarterfinals when she demolished Christina McHale in straight sets 6-2, 6-1.
After outlasting Elene Vesnina in the first round in a 2 hour 37 minute marathon in temperatures above 40 degrees Celsius (104 F), Cornet took full advantage of the much cooler conditions Tuesday and raced through the match in just 81 minutes.
"I'm very happy with the way I played today — it was a really good-quality match," Cornet said.
"I didn't make a lot of unforced errors and I hit a lot of winners.
"I was applying the right tactics, so it was great to play this way."
Cornet will play either second seed Dominika Cibulkova or China's Zhang Shuai in the quarterfinals.
"It will definitely be a tough battle but when I see the way I play today it gives me a lot of confidence for the rest of the tournament."
Earlier, Australian teenager Destanee Aiava created a slice of history when she became the first player born in the 2000s to win a main draw match on the WTA Tour.
The 16-year-old Aiava beat fellow qualifier Bethanie Mattek-Sands of the US 2-6, 6-3, 6-4 in a rain-delayed first-round match.