France's Simon, the 26th seed, defeated Spanish fourth seed David Ferrer, who became the first top 10 men's seed to be shown the exit when he fell 6-3 3-6 6-1 6-3 in the third round on a hot, humid day at Flushing Meadows.
But it was the women's fourth-round match-up between Sharapova and Wozniacki that stole the show at the US National Tennis Center.
The 10th-seeded Wozniacki, who ruled as world number one for 67 weeks but never won a grand slam crown, showed great grit in battling to a 6-4 2-6 6-2 victory over fifth seed Sharapova in a two hour 37 minute slugfest in sweltering conditions.
"It means so much to me," Wozniacki told the Arthur Ashe Stadium crowd. "It's been a bit up and down year for me. To win against a champion like Maria is an unbelievable feeling."
Victory sent the 24-year-old Dane to her first grand slam quarter-final since the 2012 Australian Open, a stretch of 11 events, with Italy's Sara Errani awaiting as her opponent.
Errani, the 13th seed, ended the rejuvenated run of 32-year-old Mirjana Lucic-Baroni of Croatia 6-3 2-6 6-0 in their fourth-round match.
Shortly after Wozniacki's victory, the remainder of the day session was ruled over due to lightning and heavy rain. Second seed Roger Federer's match against Spain's Marcel Granollers was suspended with the Swiss master trailing 5-2 in the first set.
Before the deluge, Wozniacki used stellar footwork and notable fitness to stymie Sharapova, who was forced into a slew of 20-stroke rallies that fit the Dane's game plan.
"I thought she played really well," said a disappointed Sharapova. "She made me hit a lot of balls. That's always been her strength. But she did extremely well today. She's a great retriever."
Wozniacki, who is training to run this autumn's New York City Marathon, won the hard-fought first set by breaking Sharapova in the last game.
Sharapova dominated the second set to level the match at one set apiece when officials gave the players a 10-minute break invoking the heat rule.
SPECTACULAR POINT
Once they returned to the court, Wozniacki took charge.
The critical break in the third set came after a spectacular point when Wozniacki three times raced across the baseline to retrieve in miraculous fashion, with Sharapova netting a backhand volley on the last shot to fall beind 3-1.
Wozniacki broke Sharapova again for good measure in the final game.
A slew of upsets in Wozniacki's half of the draw make her possible passage to the final a bit less daunting with second seed Simona Halep, fourth seed Agnieszka Radwanska and sixth seed Angelique Kerber already removed.
It was an emotional triumph for Wozniacki, who has had a tumultuous year in her personal life.
Her slide down the rankings starting a couple of years ago coincided with her dating and subsequent engagement with major golf champion Rory McIlroy.
This year the Northern Irish golfer called off their wedding days after invitations were mailed.
Asked if she would skip further Sunday training for November's marathon run, Wozniacki said: "I think this afternoon I'm just going to take a nice bath, have a massage and chill. And I think I deserve to have some chocolate or something."
FERRER FALLS
Simon, who had lost five of six matches against Ferrer, turned the tables on the Spaniard who had advanced to the third round through a walkover against Australian Bernard Tomic.
Rather than looking refreshed, the Spaniard was off his game and appeared exhausted. By the end, Ferrer was hunched over between points, dripping in sweat before the Frenchman finished off the nearly three-hour match.
"David is always fighting until the end," said Simon. "I just stayed relax today and had nothing to lose."
Simon advanced to a fourth-round match against Croatian 14th seed Marin Cilic, a 6-3 3-6 6-3 6-4 winner against 18th seed Kevin Anderson of South Africa.
Errani played deft defense to thwart the 121st-ranked Lucic-Baroni, who had bounced Halep in the third round.
"I like to run. I love running, so I try to be consistent to run, to be in every point, fight a lot," said Errani. "Others have a lot more good shots than me, but I try to stay there and try my best."
Her best was good enough to end an inspired run by Lucic-Baroni, who made her best slam advance since reaching the 1999 Wimbledon semi-finals.
The winners/unforced errors ledger illustrated: Lucic-Baronia had 46 winners and 64 errors, Errani struck four winners and made nine unforced errors.
"This has been a great two weeks, the best so far since I can remember for a long time," said Lucic-Baroni. "Today I felt like I ran out of gas a little bit.
"Today I felt like my body...just kind of broke down a little everywhere. I have blisters, tapes, pain everywhere in my body, so I burned out a little bit today."
