French Open champion Ostapenko was not at her best, spraying the court with 44 unforced errors and having her serve broken six times on a windy day at Crandon Park, but she still managed to win a roller-coaster ride 7-6 (7-3) 7-6 (7-5).
Danielle Collins produced the performance of a lifetime and pulled off an almighty shock at the WTA Miami Open on Wednesday night, sending Venus Williams crashing out 6-2, 6-3 to reach the semi-finals.
Stephens made short work of her opponent in the deciding set taking it 6-1.
"I knew I had to be aggressive and when I got the chance I really went for it", Ostapenko said.
The US Open champion again ended former world No.1 Victoria Azarenka's hopes of a fairytale comeback by beating her 3-6 6-2 6-1 to reach the Miami decider.
Asked if she was surprised to see a 24-year-old college graduate winning high-level matches at this stage of her career, Williams said: "There's more than one way to skin a cat".
In a men's quarterfinal, 16th-seeded Pablo Carreno Busta wasted two match points on his serve in the second set before recovering - almost two hours later - and ousting No. 6 Kevin Anderson 6-4, 5-7, 7-6 (6) in a rematch of a U.S. Open semifinal from a year ago. "We used to come down here all the time and play when I was younger".
Ostapenko, meanwhile, was delighted to reach her first WTA premier mandatory final - and just like Stephens, she is yet to win one having lost in the semi's in Beijing past year.
"I love to play in matches like this", a visibly tired del Potro said.
Stephens dropped the first three games against Azarenka, needing only 11 minutes to get into trouble.
Zverev beat Borna Coric 6-4, 6-4.
Stephens was raised in Plantation, around an hour north of Key Biscayne and is expecting her friends and family to turn up in "full force".
Alexander Zverev remains on target for his third ATP Masters title after dismantling Borna Coric 6-4, 6-4 to set up a meeting with Pablo Carreno Busta for a place in the men's final.
Following the win, Collins said that she has an incredible respect for Venus, but she is happy to focus on her game and eventually come out victorious.
The Miami Open isn't ending, but it's moving about a half-hour's drive north to the Miami Dolphins' stadium next year. But I think it'll be cool.
Alexander Zverev (4), Germany, def. Borna Coric (29), Croatia, 6-4, 6-4. "It's going to be important that I recover physically and mentally because that was a real battle".