Vandeweghe earlier beat Sabalenka, 7-6 (5), 6-1, to give the United States a 2-1 lead.
Kathy Rinaldi, in her inaugural season in charge of the Americans, became the first female captain to lead a Fed Cup team to a title since Billie Jean King with the U.S. in 2000.
“It’s been an incredible ride thanks to these ladies,” Rinaldi said. “We’re family and we’ve had each other’s backs. This was a very tough match.”
The United States holds the most Fed Cup titles in the international team competition. This was its fourth Fed Cup final since 2000; it lost the 2003, 2009 and 2010 finals.
Belarus was making its first appearance in a Fed Cup final.
“We are really satisfied we gained this result,” Belarus Captain Eduard Dubrou said. “Today’s match has showed we have a good team because last time we faced the team of U.S.A. it was 5-love and today we were really close to a good result for us.”
Vandeweghe proved the difference between the two teams. She won all eight Fed Cup matches she played this season — six singles and two doubles. Vandeweghe is the first player to win eight matches since the current eight-team World Group format was introduced in 2005.
“I had a great time out there,” Vandeweghe said. “I really relished in that moment of having the crowd against me and firing myself up and believing in myself.”
Vandeweghe, 25, is also the first player to win the maximum six Fed Cup singles matches in a year since Petra Kvitova for the Czech Republic in 2011.
Stephens has lost six matches since winning the U.S. Open in September. She lost both singles matches here, including to Sabalenka on Saturday.
Against Vandeweghe, Sabalenka had an opportunity to take an early lead when leading by 5-4 but failed to take advantage of a set point on Vandeweghe’s serve in the 10th game.
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 winner.
Vandeweghe then jumped out to a 5-0 lead before Sabalenka won her only game of the second set.
“I know she was going to keep swinging,” Vandeweghe said. “I know what I had to do and knew what I expected she would do. I just kept the pressure on.”