Vandeweghe faces Sabalenka and Stephens meets Sasnovich in the reverse singles on Sunday as the US look to get back on track in the hunt for an elusive 18th title.
It was the United States' record 18th Fed Cup crown.
Vandeweghe and Rogers trailed 5-2 in the second set with their Belarus opponents serving to level the match at one-set apiece in the eighth, 10th and 12th games. Rogers won both of her service points in the tiebreaker for a 3-2 edge and then delivered a backhand volley victor against Sabalenka's service point for a 4-2 advantage for the Americans.
Sasnovich had beaten Stephens 4-6, 6-1, 8-6 to deadlock the World Group final at 2.
On the opening day Vandeweghe put U.S. into the lead with a 6-4, 6-4 win over Sasnovich, while Sabalenka beat Stephens 6-3, 3-6, 6-4 to pull the scores level at 1-1.
Kathy Rinaldi, in her inaugural season in charge of the Americans, became the first female captain in the tournament to lead a Fed Cup team to victory since Billie Jean King for the USA in 2000.
So, the final of the Federation Cup starts on Saturday at 14.00.The beginning of the first match is 14:30 -. The U.S. last won the Fed Cup 17 years ago while Belarus are playing their first final.
Vandeweghe was drawn to face Aliaksandra Sasnovich in the first singles match.
In the deciding set, Stephens led 5-2 before Sasnovich, 23, roared back with four straight games before eventually closing it out 8-6 as Stephens suffered her sixth straight defeat since winning her maiden Grand Slam title in NY in September.
Earlier, Vandeweghe beat Sabalenka 7-6 (7-5) 6-1 to give the United States a 2-1 lead.
Sabalenka led 4-1 in the tiebreaker but surrendered her lead to a more measured Vandeweghe, who clinched the first set when the Belarussian blasted a forehand wide while going for a victor.
Stephens bounced back in the second set using the strategy that served her well at Flushing Meadows - getting balls back into court and counting on Sabalenka making unforced errors.
"I had a great time out there", Vandeweghe said.
"She did what she's supposed to do and did what I expected her to do - just swing and pray for it to go in and she did".
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