In an enthralling battle over two hours and 24 minutes, fourth-seeded American Pegula emerged with a 7-6(3), 5-7, 6-3 win to seal a place in Saturday's final against world number one Aryna Sabalenka.
Sabalenka blasted her way into the final with a 6-2, 6-2 demolition of Italy's Jasmine Paolini.
The 19-year-old Eala, ranked 140th in the world, had only two WTA main draw victories to her name before arriving in Miami.
She proceeded to beat three Grand Slam winners in Jelena Ostapenko, Madison Keys and world number two Iga Swiatek.
The lowest-ranked semi-finalist in the tournament's history, Eala seriously threatened to go one step further with another accomplished and effervescent display.
The tide looked to have turned against her when Pegula broke to go 3-1 up in the second set, but Eala broke back and her fist pump and look of determination was a sign of things to come.
Eala broke Pegula three times in the set and was broken twice herself but crucially was able to hold when serving for the set at 6-5.
Both players protected their serve better in the deciding set but Eala's forehand let her down when the American broke to go 5-3 up and she served out for a victory that brought her visible relief.
"Of course there is disappointment right after the match," said Eala.
"But there are just so many times in tennis where you have to dig through the dirt to look for the positive and I'm just enjoying because there is so much positive around me and I don't know how many times that happens," she added.
Playing with a strapped thigh from the outset, Eala turned her ankle mid-way through the second set but said she had not been impacted by the injury.
"I literally gave everything I had, I'm half tape, I'm like a mummy. I did everything and I have no regrets," she said.
"To have a week like this, the stars need to align and they did this week, and hopefully I can keep that up - that is my goal now, to keep this up," she added.
Pegula said it had been difficult to play an opponent like Eala.
"I let her back in the match at 3-1 up (second set) and she just started ripping her balls, going for her shots and you just have to weather the storm with people like that. She competes really well," said the American.