Raducanu stars for Great Britain as they knock out BJK Cup holders Canada
They will play Slovakia for a place in the final on Tuesday. Poland and Italy will face off in the other semi-final on Monday.
Raducanu broke in the first game as she started off with a bagel against Rebecca Marino, who made her debut in the event in 2011.
The second set went with serve until the 2021 US Open champion broke to lead 6-5 before wrapping up a 6-0, 7-5 victory to give her team a 1-0 lead in the contest.
Boulter then sealed their last-four spot as she beat Leylah Fernandez 6-2, 6-4.
"I know how tough she is to beat, I know what a fighter she is. She makes it so hard to close matches out," Boulter said of Fernandez.
Fernandez had won 16 of her previous 17 Billie Jean King Cup matches, including all eight she played last year as she helped lead Canada to the title.
"You've just got to keep going, keep believing, back yourself no matter what, not give her anything, and not show her that you're a little bit nervous," Boulter added.
"I think that's what I was at the end. But I just kept going for my shots and trusted them and managed to get it done the second time."
Britain are one of only four nations - alongside Australia, France and Italy - to have competed in the tournament every season since it was launched in 1963.
However, they are the only one of those teams to have never lifted the trophy, losing in four finals.
"I definitely wouldn't be here if I didn't believe we could win the tournament. I think we have got a great team. We've always got a great chance. We're going to be in with the last four," Boulter said.
