The American claimed her first title since the US Open a year ago with a 7-6 (7-5), 6-1 win over her Latvian opponent.
After Svitolina saved three consecutive match points in the second set tiebreak, Ostapenko hammered her 41st victor, a crosscourt backhand, on match point to end the almost two hour contest. She also extends her impressive undefeated record in finals to 6-0.
There's a fair gap between No. 10 and the top players; for example, she's more than 1,000 points behind No. 8 Venus Williams.
Ostapenko is an aggressive baseliner, and often batters a fearless ball, using her change of direction to hit solid winners. For her, the months after the French Open title have featured some bumps in the road. The difference, in the end, came down to those errors: Stephens defended the better, forcing her opponent to go for too much too soon.
"I knew that I was just going to have to run a lot of balls down", Stephens said of the final.
Can Stephens learn to win when she does have expectations of success?
There were eight breaks of serve in the first set alone, with French Open champion Ostapenko hitting 29 unforced errors and US Open champion Stephens making just three winners.
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The 25-year-old world number 12 beat 20-year-old world number five Ostapenko in their first ever meeting to lift the 2018 Miami Open title in style.
"I made sure after Australia I got in the best shape possible".
"I wasn't expecting a title here or anywhere, really".
The victory will be even sweeter for Stephens come Monday as she'll make her long-awaited Top 10 debut, landing at World No.9.
Perhaps with good reason, both began edgily, each going for winners, each firing errors, and both struggling to find their first serves with any consistency. "Hopefully I can make some dents there, as well, during the clay court season".
Yet another hopeless service game - at this point Stephens had been successful with just 18% of her second serves - sent the match into a tie-break which was won when the Latvian sent a backhand into the net.
Ostapenko said she followed coach David Taylor's advice to stay on the attack against the defensive-minded Svitolina even when she was having trouble with her accuracy.
It's something I really look forward to. 'I was thinking that my life was over because the only thing I had was tennis and that was the only thing that I knew, ' Stephens admitted.