Lucic-Baroni ousted second seed Simona Halep, Italy's Sara Errani posted her first career win over Williams and Swiss teen Belinda Bencic ousted sixth-seeded German Angelique Kerber on a sunny day that opened up the women's draw.
Croatian Lucic-Baroni, a 32-year-old qualifier ranked 121st in the world, dismissed Romania's Halep 7-6 (6) 6-2 to reach the fourth round for her best grand slam result since a 1999 run to the Wimbledon semi-finals.
With nothing to lose, Lucic-Baroni cut loose and rifled in 31 winners against Halep, who was on the defensive throughout the 94-minute match.
"It's amazing. I finally been able to play the tennis that I love to play. You know, being really aggressive and consistent at the same time," said Lucic-Baroni.

Bencic, 17, last year's French Open and Wimbledon junior champion, defeated Kerber 6-1 7-5 to reach the round of 16 in her U.S. Open debut.
The Swiss, who made it to the third round at Wimbledon, vowed not to be satisfied with her Flushing Meadows success.
"I want more," said Bencic.
Lucic-Baroni's next opponent will be 13th seed Errani, whose passage into the round of 16 was not as startling as the Croat's  dismantling of a world number two 10 years her junior, but a surprise nonetheless.
Errani, loser of all three previous singles matches against Williams in straight sets, outdueled the seven-times grand slam winner in a thrilling third-set tiebreaker to win their roller-coaster clash 6-0 0-6 7-6 (5).
Two other veterans also advanced.
Ninth-seeded Jelena Jankovic of Serbia, 29, crushed Sweden's Johanna Larsson 6-1 6-0, and 28-year-old Peng Shuai of China registered another upset.
The 39th-ranked Peng, who upset fourth seed Agnieszka Radwanska in the second round, eliminated 28th seed Roberta Vinci of Italy 6-4 6-3.
Also advancing was 10th seed Caroline Wozniacki of Denmark, a 6-3 6-2 winner against 18th seed Andrea Petkovic of Germany.
Williams served for the match against Errani at 5-3, but the 27-year-old Italian broke the big-serving, 34-year-old American for the third time in a topsy-turvy third set to bring the match back on serve and set up a climactic tiebreaker.
After the hot-and-cold opening to the match, the longtime doubles adversaries went toe-to-toe with long rallies and exciting exchanges that often culminated at the net.
In the third-set decider, the Italian took a 5-2 advantage before Williams rattled off three points in a row to tie it.
Then in the point of the match, Errani reached match point after a sensational trade of volleys and drop shots on a backhand volley winner into the open court that brought both an ovation from the Arthur Ashe crowd.
Errani finished the two-hour clash on her first opportunity with a crackling forehand cross court winner that allowed her to celebrate with fists pumping and a roar of triumph.
"That was a really tough match," said Errani, who won 11 of 14 points she contested at the net. "Even though I won the first set 6-0, I tried to give everything I have, focus on every point."
On the men's side, fourth seed David Ferrer of Spain reached the third round without lifting his racket when Australian Bernard Tomic withdrew with a hip injury.
The highest-ranked casualty was Ernests Gulbis of Latvia, the 11th seed, who was ousted by 45th-ranked Dominic Thiem of Austria 4-6 3-6 6-4 6-3 6-3.
Bulgarian seventh seed Grigor Dimitrov breezed into the third round with the loss of five games against Israel's Dudi Sela, while sixth-seeded Czech Tomas Berdych was taken to five sets and three hours 45 minutes by Martin Klizan of Slovakia.
Twelfth seed Richard Gasquet and 20th-seeded Gael Monfils both advanced in straight sets to set up an all-French collision for a berth in the fourth round.
Working harder was 18th-seeded South African Kevin Anderson, a four-set winner against Jerzy Janowicz of Poland, while Spain's 19th seed Feliciano Lopez won a fourth-set tiebreaker to advance past Japanese qualifier Tatsuma Ito.

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