The South American ranked 24th in the world beat her third top-10 opponent this season, but notched her first career win over a world number one as she clawed out the victory in three hours.
Haddad Maia, who won titles at Nottingham and Birmingham in June, became the first Brazilian to reach the quarters at a WTA 1000 tournament.
She was the first from her country even to face a number one since Telian Pereira lost to Serena Williams at Roland Garros in 2016.
Swiatek, whose six titles this season include the French Open, missed her chance at a 50th match win this season.
Her run of 23 straight wins at the Masters 1000 level was snapped.
Haddad Maia put Swiatek on the defensive, forcing her to save 15 of 19 break points while committing nine double-faults.
She limited her own unforced errors to a dozen, backed up by 23 winners while Swiatek ended with 33 winners and 28 unforced errors.
In other third-round action, Coco Gauff survived 15 double-faults to squeeze out a 7-5, 4-6, 7-6 (7/4) win over Aryna Sabalenka.
The American teenager contributed just under half of the miscues in the error-strewn affair, with her opponent accounting for 18 additional doubles.
Tenth seed Gauff, who fell to Swiatek at Roland Garros in her first Grand Slam final this year, battled for three and a quarter hours against sixth-seeded Sabalenka.
Gauff finished with nine aces and saved 10 of 14 break points that she faced.
"It was a difficult match for both of us," Gauff said. "We were both struggling with the serve.
"The conditions weren't easy today, a lot of wind. I think I hung in there mentally and that's what I'm most proud of."
Victory for the 18-year-old came a day after she beat Wimbledon champion Elena Rybakina in the third round in a match that took two and three-quarter hours.
The American admitted that trailing 3-0 in the final set, she had to give herself a serious talking-to.
"I said if I was going to lose, I'm not going to lose like this. I had to change, and that's what I did.
"I was being too negative on myself. She is frustrating to play. She plays big tennis -- sometimes you hit a good shot and she hits a winner."
Gauff added: "There's a reason why she was number two in the world."
Gauff will face off on Friday against two-time Grand Slam winner Simona Halep after the former number one from Romania defeated Switzerland's Jil Teichmann 6-2, 7-5 in 91 minutes.
Seventh-seeded American Jessica Pegula advanced, beating defending champion Camila Giorgi of Italy 3-6, 6-0, 7-5.
https://sports.yahoo.com/swiatek-ambushed-brazils-haddad-maia-234217965.html
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