They have now won the Fed Cup 18 times, extending their lead over the Czech Republic/Czechoslovakia, who have 10 titles.
In a tense conclusion, the hosts broke Rogers again but the American pair would not buckle despite the intense atmosphere of a Minsk crowd desperate to see a first home Fed Cup triumph. "CoCo (Vandeweghe) came out and just played unbelievable".
"I'm ready for a vacation".
In the second set Belarus team was leading 5-2, wasted two set points on 5-4, served to take it to a decider on 6-5 but United States prevailed in the tie-break dominating.
Sasnovich had kept Belarus alive after beating US Open champion Sloane Stephens 4-6 6-1 8-6 to leave the final level at 2-2 on the indoor hard-court Chizhovka Arena.
"I'm just really thrilled for all four players", said United States captain Kathy Rinaldi. "We're going to have each other's backs and compete as a really tight-knit team".
The U.S. holds the most Fed Cup titles in the worldwide team competition. This was its fourth Fed Cup final since last winning in 2000. United States had lost all the last three finals played, in 2003 to France, in 2009 and 2010 to Italy.
So, the final of the Federation Cup starts on Saturday at 14.00.The beginning of the first match is 14:30 -. "Today's match has showed we have a good team because last time we faced the team of U.S. it was 5-love and today we were really close to a good result for us".More news: Hulu and Nintendo bring streaming service to the Switch
Vandeweghe proved the difference between the two teams. On Sunday two singles and a doubles match are planned.
Alexandra Sasnovich will play against Coco Vandeweghe.
"I had a great time out there", Vandeweghe said.
Stephens had lost six matches since winning the U.S. Open in September.
Stephens served for the match against Sasnovich at 5-3 in the third set, but was unable to clinch the title for the United States.
World number 10 Vandeweghe put in a composed performance against Aliaksandra Sasnovich to send the visitors ahead with a 6-4 6-4 victory.
Sabalenka led 4-1 in the tiebreaker but surrendered her lead to a more measured Vandeweghe, who clinched the first set when the Belarusian blasted a forehand wide while going for a victor.
"I know she was going to keep swinging", Vandeweghe said.
"And then it showed in the second set, she withered when I kept the pressure on her, and then I just closed it out".