A more aggressive Svitolina went for her shots and clawed back into the contest. Svitolina missed on some key moments that opened the door for Stephens to commit to her serve and clinch a 3-0 hold.
But Stephens sealed the set when her opponent could only find the net with a backhand from deep behind the baseline. She faced the challenges that were alive and well with the 25-year-old, who nearly forced deuce but erred the ball into the net to make it 3-1.
She saved three break points in the sixth game but was unable to convert two chances of her own in Stephens' next service game.
Stephens is now 2-2 against Svitolina all time. After winning her first Grand Slam at the 2017 US Open, Stephens reached the final of this year's French Open but fell in the first round of the Australian Open and Wimbledon.
"I know that I won lots of finals but for me every final is a big challenge".
Despite the challenges from the American, Svitolina found ways of taking charge to capture the set in the eighth that closed out 49 minutes, with both coaches coming out to speak to the players.
"That's definitely a good statement for myself", Svitolina told reporters. Even though she still struggled on serve, Svitolina attacked on return and broke twice to wear down a suddenly passive Stephens.
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The 24-year-old's momentum continued as she produced an astounding run down victor to break Stephens in the second game.
But the American continued to pound away at the corners to maintain her break advantage. Nothing's working. But then I won one game.
"It's a very special moment for me", said Svitolina to Andrew Krasny during the trophy ceremony. "I played against top players and the best players in the world, and I played great tennis", she said.
"Actually, I thought about it when I lost the first set and I was like, "Oh, my God, I'm never going to say this again", she added with a grin.
Svitolina's form nosedived in the second half of the year and after sneaking into the eight-woman field courtesy of three early-season titles, the world number seven sensed her presence had been regarded as undeserved in some quarters.
Roger Federer is still third after his 99th career title at Basel, while runner-up Marius Copil of Romania soared to a career-high 60th after shooting up 33 places.
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