The 16th seed Alexandrova played brilliant attacking tennis from the outset to beat the Pole and leave the WTA tournament without any of the top three seeds in the quarter-finals with Aryna Sabalenka and Coco Gauff also out.
France's Caroline Garcia upset world number three Gauff beating the American 6-3, 1-6, 6-2 on Monday to advance to the quarter-finals of the Miami Open, while world number two Aryna Sabalenka had been eliminated by Ukraine's Anhelina Kalinina on Saturday.
Swiatek never looked comfortable after Alexandrova broke her in the opening game and took control of proceedings with some outstanding, attacking tennis.
Swiatek generated just one break point in the match but Alexandrova saved it to take a 4-2 lead in the second set.
Having come from a set down in the previous round against Linda Noskova, Swiatek would have had some belief in turning the contest around but her Russian opponent was in no mood for mistakes.
She made short work of the second set, breaking to go 2-1 up with a startling cross-court return and ending the match with 31 winners to Swiatek's 11.
The match was the first in which Swiatek has not broken serve since her defeat to Ash Barty in Adelaide in January, 2022.
Alexandrova laughed off the suggestion that she had played a perfect match but was certainly not going to downplay her performance.
"It was such a great game for me in consistency, the serve, the returns, the playing from the baseline, I think it was pretty good and I hope I can keep for the next match," she said.
A quarter-finalist also in Miami last year, that next match will be against fifth-seed Jessica Pegula on Wednesday.
