The 14th-seeded Swiss proved a frustrating obstacle for Swiatek, with the four-time Grand Slam champion struggling to master her opponent for the majority of what proved an intriguing tussle on Centre Court.
As the evening gloom set in, Swiatek eventually got a handle on her opponent's game, moving clear in the final set before wrapping up a 6-7(4) 7-6(2) 6-3 victory after more than three hours of compelling twists and turns.
Olympic gold medalist Bencic had been stubborn in her resistance in the opening set, saving six break points before taking it on a tiebreak and then fighting back after falling behind in the second.
But Swiatek saved two match points at 5-6 in the second and then levelled the contest in another tiebreak.
The top seed, who arrived at the All England Club having won her third French Open title last month, had never reached the last eight at Wimbledon in her previous three attempts and will next face Ukrainian wild card Elina Svitolina.
Should the Pole go on and win Wimbledon, Swiatek will be in exalted company with only Venus Williams in 2005 and her sister Serena four years later ever lifting the trophy after facing match point en route to the title in the Open era.
"I don't know if I even came back from match point down in my career," Swiatek said in her on court interview. "I feel I needed the win to believe in myself on this surface."
"It's actually a little bit easier because on the other hand you feel like she's leading anyway so you play those shots more fearlessly because you know you have nothing to lose."
SWIATEK FRUSTRATED
Swiatek had not dropped a set in her previous three matches at the tournament but any thoughts that she would face a similarly smooth ride against Bencic were quickly dispelled.
While the Pole seemed untroubled early in the first set, winning 17 points in a row on serve, and generating break points almost at will, her frustration levels started to mount as Bencic refused to yield.
Her six break points in the first set included two set points but Bencic doggedly resisted and then raced into a 6-1 lead in the tiebreak, eventually closing it out when the world number one fired a forehand long.
Swiatek would have been forgiven for thinking it was not going to be her day when Bencic saved a seventh straight break point in the first game of the second set.
But on the very next point, she finally made one stick, guiding a forehand down the line to grab a first break of the match.
Bencic broke back in the sixth game and then moved to the brink of victory with two match points on the Swiatek serve at 6-5 in the second set.
The Pole saved both and then finally swung momentum in her favour as she dominated the tiebreak to level the match.
It then got more comfortable for Swiatek as Bencic dropped serve with a double fault to fall 3-1 behind, a deficit that she could not turn around.
While Swiatek may be more at home on the Parisian clay, she is seemingly starting to warm to Wimbledon's slick grass courts.
"My love is getting bigger and hopefully I am going to have as many days as possible on this surface," she said. "This is my best year on grass and the hard work is paying off."
