CoCo Vandeweghe won the final 10 games to beat Germany's Andrea Petkovic 3-6 6-4 6-0 on Sunday and give the United States an insurmountable 3-0 advantage in their Fed Cup quarter-final match.
The US advanced to the semi-finals for the first time since 2010.
The fourth singles match was cancelled, and the doubles match was set to be played later on Sunday.
The US will host defending champions Czech Republic in the semi-final to be played April 22-23 at a venue to be announced. The Czech Republic beat Spain 3-2. The final is set for November.
Vandeweghe, the world's 20th-ranked player, put the US ahead 2-0 earlier in the day when Julia Goerges retired with an injury in a match that was halted by rain Saturday with Vandeweghe ahead 6-3 3-1.
Vandeweghe gave credit to the sun-baked Maui crowd, one day after rain pelted the court.
"You guys pulled me through, that's the bottom line," she said.
Vandeweghe was suffering from cramps in the second set.
"I was just trying to manage, that was basically it, and keep persevering," she said.
Alison Riske put the Americans ahead in the first match on Saturday with a 7-6 (12-10) 6-2 victory over Petkovic.
Meanwhile Belarus, without former world No.1 Victoria Azarenka who has taken time off to have a baby, beat the Netherlands 4-1 to book a semi-final berth against Switzerland.
Aliaksandra Sasnovich is ranked 104 places below No.24 Kiki Bertens, but didn't let it show as she broke her Dutch opponent's serve seven times in a 6-3 6-4 win.
Next up on Sunday was 18-year-old Sabalenka, who beat veteran Michaella Krajicek 7-6 (7-5) 6-4 and put Belarus in the semi-finals for the first time with an insurmountable 3-1 lead.
Belarus finished off a strong weekend in the remaining dead-rubber doubles match when Olga Govortsova and Vera Lapko won 6-4 6-2 against the Dutch duo of Cindy Burger and Arantxa Rus.