A 17-year championship drought has come to an end for the United States when they overcame hosts Belarus 3-2 to win a record-extending 18th Fed Cup title.
Sasnovich had earlier beaten US Open champion Sloane Stephens 4-6 6-1 8-6 in a thrilling match to force a decider.
She broke again in the first game of the second set, and although Sasnovich levelled things up immediately, Vandeweghe struck back before holding to love to take control.
The Americans dominated the tiebreaker, winning five of the last six points.
Vandeweghe earlier beat Sabalenka 7-6 (5), 6-1 to give the US a 2-1 lead.
It is the first U.S. victory since the team of Lisa Raymond, Lindsay Davenport, Monica Seles and Jennifer Capriati in 2000. Belarus is playing in the Fed Cup final for the first time. She is the first player to win eight matches since the current eight-team World Group format was introduced in 2005.
Alexandra Sasnovich will play against Coco Vandeweghe.
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. She lost both singles matches here in Minsk, including to Sabalenka on Saturday.
Earlier on Sunday, Vandeweghe put the United States of America 2-1 up by beating Sabalenka 7-6 (5), 6-1, while Sasnovich battled back from a set down to beat Sloane Stephens 4-6, 6-1, 8-6 to draw Belarus level at 2-2.
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.
After U.S. Open champion Sloane Stephens dropped her singles match for the second straight day, this time to deadlock the match at 2, it came down to Rogers and Vandeweghe.
"We know we're going to have a very competitive weekend", Rinaldi 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. I just kept the pressure on".