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Jabeur lost four games in a row from a position of strength to concede the opening set on Court Two but responded in sensational fashion to outplay last year's French Open champion.
The 26-year-old has now beaten three Grand Slam champions so far here, taking out five-time Wimbledon winner Venus Williams and Spain's Garbine Muguruza during her impressive run.
In doing so she has endeared herself to the Wimbledon crowds with a wily game full of variety but also power when required.
Jabeur will contest her second Grand Slam quarter-final on Tuesday against Belarusian second seed Aryna Sabalenka, having reached her first in Australia in 2020.
When Swiatek struck a majestic backhand winner down the line to take the opening set it seemed that the Pole was beginning to take charge of a match in which she started nervously.
But Jabeur started the second set like a woman on a mission, breaking to love in the opening game then holding her own serve with a trademark dropshot that had Swiatek slamming her racket into the net tape in frustration.
It was a sign of things to come as Jabeur broke serve again in the next game with a belting forehand winner at the end of a long baseline exchange. The Tunisian then saved three break points, one with an ace, to lead 4-0.
Swiatek's serve began to look vulnerable and on set point down she rolled in a 66 mph delivery that Jabeur nonchalantly dinked over for a winning dropshot.
There was no stopping 21st seed Jabeur in the decider after a Swiatek double fault gifted her a 3-1 lead. Serving for the match at 5-1 she showed no nerves, sealing a win with an ace and receiving a warm ovation from the crowd.
Afterwards she revealed she had one very special fan. "Actually I got congratulated by Roger (Federer) after my match, which was amazing. I think now I'm good in my tennis career. That inspires me a lot and gives me the hunger to win more."
Federer oldest man to make quarterfinals
Meanwhile, Federer weathered a first-set storm to become the oldest man in the Open Era to reach the quarter-finals with a 7-5 6-4 6-2 win over Italian 23rd seed Lorenzo Sonego on Monday.
The Swiss, who will turn 40 next month, was deadlocked at 5-5 in the first set when a torrential downpour sent the players back into the locker room with Sonego down break point.
The 20-minute disruption, during which the roof was closed over a soggy and windswept Centre Court, did Sonego no favours as he immediately produced a double fault under the floodlights to surrender his serve.
That provided Federer with the spark he needed to motor through the rest of the contest after converting only two of the nine break points he had earned during the first set.
In his record-extending 18th Wimbledon quarter-final, and 58th across all four majors, the eight-time All England Club champion will meet either Russian second seed Daniil Medvedev or Poland's Hubert Hurkacz, whose match will resume on Tuesday.
Kerber wins generation game
US teenager Coco Gauff's hopes were dashed by Germany's former champion Angelique Kerber as she went down 6-4 6-4 in a Centre Court battle of the generations on Monday.
The 33-year-old Kerber showed all of her vast experience to keep Gauff (17) at bay as she reached her first Grand Slam quarter-final since winning the title here in 2018.
Gauff had not lost a set in matching her run to the fourth round on a startling debut in 2019, but the American was given a lessen in clinical efficiency by the left-hander.
Barty survives scare
The serve was not at full throttle and the strokes were often rather wayward, but that did not stop Australian Ash Barty from reaching the quarters for the first time with a 7-5 6-3 win over French Open champion Barbora Krejcikova.
Barty had been expected to easily make her greater grasscourt pedigree count. Yet she was the one who came unstuck first with Krejcikova threatening to win her 16th match on the trot after seizing the early initiative when she broke for a 2-1 lead in the first set.
A flurry of breaks midway through the second set failed to fluster Barty and, after sealing victory with a thumping ace, she puffed her cheeks before breaking into a smile - the relief at finally climbing over that fourth round hurdle clear to see.
The 25-year-old will next face either 338th-ranked British wildcard Emma Raducanu or fellow Australian Ajla Tomljanovic, the world number 75, for a place in the semis.
Djokovic rolls on
It was business as usual for top seed Novak Djokovic as the Serbian dismantled the challenge of Chile's Cristian Garin with a 6-2 6-4 6-2 victory to reach the last eight and keep his title defence intact.
The world No 1, who won the last two men's singles titles at the All England Club, will play his 50th Grand Slam quarter-final when he faces unseeded Hungarian Marton Fucsovics, who ousted Russian fifth seed Andrey Rublev 6-3 4-6 4-6 6-0 6-3.
Only Federer, an eight-time winner at Wimbledon, has reached more Grand Slam quarter-finals.
Canada will have two representatives in the men's singles quarter-finals here for the first time after Denis Shapovalov and Felix Auger-Aliassime both made it past the fourth round.
Shapovalov outclassed Roberto Bautista Agut and Auger-Aliassime won a five-setter against Germany's fourth seed Alexander Zverev.
Ajla Tomljanovic ended the dream run of British teenager Emma Raducanum, who quit when trailing 6-4 3-0 after failing to return from a medical timeout.
Karolina Muchova battled past Spain's Paula Badosa 7-6(6) 6-4 to reach the last eight for the second time while Viktorija Golubic upset 23rd seed Madison Keys 7-6(3) 6-3.
Russian Karen Khachanov reached his first Wimbledon quarter-final after seeing off American Sebastian Korda 3-6 6-4 6-3 5-7 10-8.
So-called Manic Monday is unique at Wimbledon with all the men's and women's last 16 singles matches on the schedule. Next year the traditional middle Sunday rest day will be scrapped and the schedule changed.