Swiatek looked down and out at 15-40 on her serve at 5-6 in the second set, but she produced her best tennis with two sumptuous winners to turn the tie around on Sunday.
The four-time grand slam champion continued to be pushed all the way by Olympic gold medallist Bencic in a tense third set before she eventually prevailed 6-7 (4-7) 7-6 (7-2) 6-3 after a three-hour epic on Centre Court.
It sent Swiatek through to the last-eight at the All England Club for the first time and having won the junior title at SW19 previously, she will march on with renewed belief this could be her year on her least favoured surface.
Top seed Swiatek had reached the fourth-round without dropping a set but experienced trouble early on against Bencic, being forced to take a medical time-out after only three games due to a blister.
Swiatek, who played two tie-breaks in the same match for the first time, said in her on-court interview: "She had match point right? So, I don't know if that ever happened in my career, being back from match point down, but I am really happy."
"Every day my love (for grass courts) is getting bigger, so hopefully I am going to have as many days as possible to play on this court."
Earlier, fourth seed Jessica Pegula progressed into the quarter-finals at Wimbledon for the first time with a straight-sets win over Ukraine's Lesia Tsurenko 6-1 6-3.
Next up for Pegula is a quarter-final clash with Marketa Vondrousova, who dug deep to win the all-Czech encounter with Marie Bouzkova 2-6 6-4 6-3.
Russian teenage prodigy Mirra Andreeva continued her fairytale event at just 16 years of age, the qualifier reaching the fourth round in her very first senior grass-court tournament.
Andreeva was nerveless as she defeated her compatriot, the No.22 seed Anastasia Potapova 6-2 7-5 to reach the last-16 where she'll face former US Open finalist Madison Keys.
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