The 19-year-old extended her historic run at the WTA 1000 event with a stunning 6-2, 7-5 victory against the world No 2 and five-time Grand Slam winner.
Eala remarkably broke Swiatek in eight of the Polish great's 10 service games and struck a host of amazing forehand winners down the line in the contest.
In her on-court interview, a stunned Eala said: "I don't know what to say. I'm in complete disbelief right now, I'm on cloud nine."
When shown a photo of her graduation from the Rafa Nadal Academy less than two years ago, with Swiatek by her side, Eala said: "It's so surreal.
"I feel like I'm the exact same person as I was in that photo. But of course, circumstances have changed! I'm so happy and so blessed to be able to compete with such a player on this stage.
"My coach told me to run, to go for every ball, to take all the opportunities I can, because a five-time Slam champion is not going to give you the win."
Eala, who is competing as a wildcard, is the first player from the Philippines to reach a semi-final at tour level.
Having entered the tournament as the world No 140, Eala will become the first player in her nation's history to break into the top 100 of the women's or men's rankings.
Eala's victory over Swiatek was her third win against a former Grand Slam champion during her run in Miami after she beat Jelena Ostapenko and Madison Keys.
The teenager has not dropped a set en route to the semi-finals, having earned four wins and also received a walkover from Paula Badosa in the last 16.
The left-hander will face the winner of the quarter-final matchup between Jessica Pegula and Emma Raducanu in the last four.
For Swiatek, the defeat has lengthened her run without winning a title and she has not reached a final since securing her fourth French Open crown in June last year.
The 23-year-old Pole has fallen at either the quarter-final or semi-final stage in all five of her WTA tournaments so far this season.