Sabalenka beat Stephens 6-3, 3-6, 6-4 Saturday after CoCo Vandeweghe earlier defeated Aliaksandra Sasnovich 6-4, 6-4 to give 17-time champion United States a 1-0 lead.
The Americans are looking to break a 17-year championship drought, while Belarus is playing in its first Fed Cup final.
Sabalenka's carefree and often careless tennis resulted in 31 winners and 57 unforced errors. She won on a fourth match point when Stephens netted a forehand.
A wild third set saw six straight breaks of serve before Sabalenka held in the seventh game.
"(It's) a good experience for me because I've never felt these emotions, playing at home and the score is 0-1," Sabalenka said.
Stephens has yet to win any of the five matches she's played since winning the U.S. Open.
"We're playing Fed Cup so anything goes," Stephens said. "I want to play like that. That was insane. Playing for her country, the crowd behind her, she played great."
Vandeweghe also faced a boisterous crowd at the indoor hard court in Minsk as she played Sasnovich for the first time.
"I think that's part of having the home court advantage and I would expect the same in the U.S.," Vandeweghe said.
Vandeweghe broke in the opening games of both sets at Chizhovka Arena, and didn't face a break point on her serve in the opener.
In the second set, Vandeweghe lost serve in the second and eighth games, but broke serve on three of four offerings to secure the match.
Vandeweghe holds a perfect record in Fed Cup action this year, winning five singles and one doubles match including her defeat of Sasnovich.
"I think there's different moments that excite you in tennis," Vandeweghe said. "For me, Fed Cup is probably one of the more exciting moments I could have in my career.
"I don't want to use the word 'ooze' confidence, but I can't think of a better word. I just take the energy that's around me and I really use it to my advantage."
The Americans won a record 17th Fed Cup title in 2000, with Billie Jean King as captain. Since then, they have played and lost in three finals - 2003, 2009 and 2010.
(This story has been corrected to show that the third set, not the second set, had six straight breaks of serve at the start.)
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