Coco Vandeweghe gave the U.S., who are seeking a record-extending 18th title, a 2-1 lead when she beat world number 78 Aryna Sabalenka 7-6(5) 6-1 in the day's first singles rubber.
Vandeweghe and Shelby Rogers will now face Sasnovich and Sabalenka to decide the winner of the international competition.
Stephens' latest defeat means she has not won a singles match since claiming the U.S. Open title on Sept. 9.
Beaten by Sabalenka on Saturday, she got off to an encouraging start against Sasnovich in the reverse singles, breaking early and staying in control to take the first set with her fourth ace of the match.
She had two break points in the first game of the second, but squandered both and few would have predicted the collapse that followed, with Sasnovich winning five games in a row before Stephens got back on the board.
The Belarusian claimed the first of three set points to level the tie.
Stephens struck a powerful forehand to go 4-2 up in the decider but stumbled again when serving for the match, allowing Sasnovich to break back.
The Belarusian in turn failed close out the match on her own serve, allowing Stephens to level at 6-6, before sealing the win by taking the next two games.
Vandeweghe, who beat Sasnovich on Saturday before Sabalenka stunned Stephens, came from behind to win a first set tie-break on Sunday before breezing through the second set.
"I know she (Sabalenka) has only got one style of play and she's just going to keep swinging," Vandeweghe said.
"I knew if I just kept giving myself opportunities and getting my nose in front in her service games I'd keep getting opportunities and she'd eventually break down."
The American is the first player to record a spotless year in Fed Cup singles rubbers since Petra Kvitova went unbeaten for Czech Republic in 2011.
(Writing by Simon Jennings in Bengaluru; Editing by Toby Davis and Christian Radnedge)
