Jabeur had never been past the second round at Wimbledon before the 2021 tournament but will now face second seed Aryna Sabalenka in the quarter-finals.
The Tunisian stormed back from behind on Court 2 to defeat seventh seed Swiatek 5-7 6-1 6-1.
Jabeur sealed her victory with a ninth ace of the match and let out a passionate roar.
She was fantastic at key moments, converting all seven of the break-point opportunities she created and firing 30 winners to 23 unforced errors.
Swiatek, by contrast, racked up 15 break-point chances but could only take three of them. The Pole only had a first-serve percentage of 46 and struggled to find her rhythm.
Jabeur, seeded 21st, also impressively saw off Garbine Muguruza in a comeback victory in the previous round.
She has now matched her best grand slam result, achieved when she reached the last eight at the Australian Open last year.
Sabalenka, meanwhile, survived a scare but ultimately prevailed in three tough sets against Elena Rybakina.
A 6-3 4-6 6-3 win in just under two hours gave Sabalenka her first-ever appearance at a slam quarter-final.