The French Open champion came out sharp and fired an unreturnable serve out wide to capture the first set before falling behind 4-1 in the second as Davis raised her level.
Despite the deficit the feisty Pole stubbornly refused to drop her first set of the tournament, winning a tense 16-shot rally to set up break points at 4-4, which she converted when Davis whacked a backhand into the net.
In the end, Swiatek’s superior serving and relentless defense carried the day against Davis, who plays a similar but less potent brand of tennis as Swiatek.
The 21-year-old top seed admitted she was not at her best during the two-hour night match on Louis Armstrong Stadium despite reeling off the match’s final five games.
“I couldn’t find my rhythm today,” Swiatek said in an on-court interview.
“She played totally differently than any other player. She played very smart. I’m pretty happy at the end that I could put balls in.
“I’m trying to enjoy every match even when it’s not perfect. Just trying to go for it. Trying to find solutions in every situation.”
Swiatek went on a blistering 37-match winning streak earlier this year to claim titles in Roland Garros, Doha, Indian Wells, Miami and Rome but cooled off this summer, losing four matches during the hard-court season.
So far in New York she has put to rest any questions about her form and will be the heavy favourite when she takes on Germany’s Jule Niemeier on Monday after the Wimbledon quarterfinalist upset China’s Qinwen Zheng 6-4 7-6(5) to reach the Round of 16.
Meanwhile, American Danielle Collins came out all guns blazing, hammering 52 winners past experienced Alize Cornet of France in a 6-4 7-6(9) victory on Saturday to book her spot in the fourth round of the U.S. Open for the first time.
In a classic contest between the contrasting styles of attack and defence, the 28-year-old Collins came out on top by firing rocket groundstrokes from both her forehand and backhand in front of an appreciative crowd in the day’s final match at the Arthur Ashe Stadium.
Collins, who finished runner-up at the Australian Open this year, will next face sixth seed Aryna Sabalenka in a battle of hardhitters for a spot in the quarter-finals.
“This is one of my favourite slams. But didn’t have my best results at this specific one,” Collins, who beat two-time former champion Naomi Osaka in her opening round, said.
“To be able to kind of have my best results that I’ve had here has been great. Obviously want to try to take it to the next level and do the best I can. With the way I’m playing, I’ve just got to take it one match at a time.”
Cornet, who was contesting her 63rd consecutive main draw at the majors and had defeated last year’s champion Emma Raducanu in her opening round, knew she had to force Collins into making errors to have any chance of a victory.
But her American opponent made few mistakes during the one hour and 53 minute contest, while managing to hit more than three times the number of winners.
A single break of Cornet’s serve in the fifth game was enough for Collins to take the opening set.
The American set up her first match point during a closely contested tiebreaker but was forced to save three set points before she could close out the match with a backhand winner at the net.
“I think if we look at Alize’s record she battles in every single match,” Collins said. “When she goes down she doesn’t go down easy. I knew I would have to follow the ball in to the net, be patient, and win points two, three, four times.”
Sabalenka spent two hours and 15 minutes on court in her previous round, during which she rallied from 5-1 down in the second set and saved two match points to beat Estonian Kaia Kanepi 2-6 7-6(8) 6-4.
It was a much easier outing on Saturday evening for the Belarusian on the final match on Grandstand court.
The former world number two, a semi-finalist at Flushing Meadows last year, steamrolled qualifier Clara Burel 6-0 6-2 in just 68 minutes, hitting 27 winners past the 21-year-old from France.
Join our commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies