Sakkari, who had lost her last four matches against Swiatek without winning a set, turned the tables on the erratic top seed in a thrilling clash, achieving what is her joint best-ever result by ranking.
It also ends a mindboggling streak from Swiatek, who had previously never lost a completed match at a 1000 event after winning the first set (109-0).
She will now face the winner of the quarter-final between Karolina Muchova and Anna Kalinskaya, as she eyes her first WTA 1000 title after reaching the finals of Indian Wells and Guadalajara in 2022.
Sakkari reached a career-high ranking of third in the world that year, but now sits at 52nd after a tough spell on tour.
"I'm speechless because it's been a while since I got a big win like today. When you are dropping in the rankings and not playing your best tennis, you are doubting yourself and think you'll never beat those players again," she said after her win.
"Last year in the second round against her, I wasn't confident or believing in myself. But this year is different and I'm feeling a lot better."
Swiatek, who has such a formidable record in Doha, winning 17 of her last 18 matches prior to today's encounter and reaching the quarter-finals in the last five editions, struggled to find her rhythm from the back of the court.
Both players started well, holding serve with relative ease. However, the Pole pounced on a sloppy few points from Sakkari at 40-15 in the fifth game, securing the break and reeling off the next four games in a row to take the opening set.
Sakkari responded well, though, snatching an early break in the second to lead 3-0. But Swiatek levelled proceedings to get back to 4-4, and looked well on her way to sealing a straight-set victory.
Yet after fending off two break points in the ninth game, Sakkari shocked Swiatek to secure the break herself and take the match to a decider. As a result, the 30-year-old ended a streak of nine sets lost in a row against her opponent.
The pair exchanged early breaks at the start of the third set, as the errors continued to flow from Swiatek's racket. On the other side of the net, Sakkari began to raise her level, taking a 5-3 lead with the opportunity to serve for the match.
The chance passed her by as she squandered a match point, but she finally managed to get over the line on Swiatek's serve, after the 24-year-old put a simple volley into the net.
Majestic Mboko beats Rybakina
19-year-old sensation Victoria Mboko produced a scintillating display to edge a nail-biting contest 7-5, 4-6, 6-4 against Elena Rybakina, ending the Australian Open champion's nine-game winning run in the process.
Down 4-2 in the final set, Mboko won four games in a row with some heavy hitting from the back of the court, snatching the initiative away from the world number three. She is into just her second WTA 1000 semi-final as a result.
She has now claimed back-to-back wins against top-10 opponents, after knocking out world number seven Mirra Andreeva in the last 16.
Mboko reigned supreme on home turf at the Canadian Open back in August to win her maiden 1000 title, and is now two matches away from a second crown at this level.
She will take on 2025 runner-up Jelena Ostapenko in the last four, who claimed a hard-fought 7-5, 6-4 victory over lucky loser Elisabetta Cocciaretto.
The former French Open champion defeated Swiatek in the semi-final last year, ending her 15-match winning run in Doha, before losing to Amanda Anisimova in the final.